Search

A scan of soft supersymmetry (SUSY) breaking parameters within the string theory landscape with the minimal supersymmetric standard model assumed as the low energy effective field theory---using a power-law draw to large soft terms coupled with an anthropic selection of a derived weak scale to be within a factor of 4 of our measured value---predicts a peak probability of ${m}_{h}\ensuremath{\simeq}125\text{ }\text{ }\mathrm{GeV}$ with sparticle masses typically beyond the reach of LHC Run 2. Such multiverse simulations usually assume a fixed value of the SUSY conserving superpotential $\ensuremath{\mu}$ parameter to be within the assumed anthropic range, $\ensuremath{\mu}\ensuremath{\lesssim}350\text{ }\text{ }\mathrm{GeV}$. However, depending on the assumed solution to the SUSY $\ensuremath{\mu}$ problem, the expected $\ensuremath{\mu}$ term distribution can actually be derived. In this paper, we examine two solutions to the SUSY $\ensuremath{\mu}$ problem. The first is the gravity-safe-Peccei-Quinn model based on an assumed ${\mathbb{Z}}_{24}^{R}$ discrete $R$-symmetry which allows a gravity-safe accidental, approximate Peccei-Quinn global symmetry to emerge which also solves the strong $CP$ problem. The second case is the Giudice-Masiero solution wherein the $\ensuremath{\mu}$ term effectively acts as a soft term and has a linear draw to large values. For the first case, we also present the expected landscape distribution for the Peccei-Quinn scale ${f}_{a}$; in this case, weak scale anthropics limits its range to the cosmological sweet zone of around ${f}_{a}\ensuremath{\sim}{10}^{11}\text{ }\text{ }\mathrm{GeV}$.

We study the correspondence between ${\mathrm{AdS}}_{3}$ massive IIA supergravity vacua and two-dimensional $\mathcal{N}=(0,4)$ quiver quantum field theories. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space that provide the dual quiver theory with exactly the correct amount of flavor symmetry in order to cancel its gauge anomalies. Then we propose that the structure of the field theory should be complemented with additional bifundamental matter, which we argue may only be $\mathcal{N}=(4,4)$ hypermultiplets. Finally, we construct a Bogomol'nyi-Prasad-Sommerfield (BPS) string configuration and use the old and new supersymmetric matter to build its dual ultraviolet operator. During this holographic synthesis, we uncover some interesting features of the quiver superpotential and associate the proposed operator with the same classical mass of its dual BPS string.

The massless three-dimensional Gross-Neveu-Yukawa (GNY) and Nambu–Jona-Lasinio–Yukawa (NJLY) models at finite temperatures are analyzed within the mean field framework considering all coupling values. When the number of Dirac fermions is taken to be Nf=1/4 (GNY) and Nf=1/2 (NJLY) these models relate to the supersymmetric Wess-Zumino (WZ) theory with cubic superpotential and one superfield. In this case the results show that the strong-weak entropy density ratio decreases from the Stefan-Boltzmann value, in the weak limit, to s/sfree=31/35 at strong couplings. This value agrees with the one recently obtained by applying the large-N approximation to the supersymmetric O(N) WZ model with quartic superpotential and N superfields. When Nf=0 one obtains s/sfree=4/5 recovering, as expected, the ratio predicted in the context of the O(N) scalar model. However, contrary to the O(N) WZ model the simple Yukawa models analyzed here do not behave as CFTs for all couplings since the conformal measure exactly vanishes only at the extreme weak and strong limits although the speed of sound indicates that the deviation, at intermediate couplings, appears to be rather small. By comparing the thermal masses behavior in each case one can trace this difference as being a consequence that in the GNY/NJLY case the fermionic mass vanishes for all couplings while within the O(N) WZ it only vanishes at the weak and strong limits. On the other hand, the Yukawa bosonic dimensionless masses display a more universal behavior decreasing from 2ln[(1+5)/2], at infinite coupling, to zero (at vanishing coupling).

We systematically study the holographic phase transition of the radion field in a five-dimensional warped model which includes a scalar potential with a powerlike behavior. We consider Kaluza-Klein (KK) resonances with masses mKK at the TeV scale or beyond. The backreaction of the radion field on the gravitational metric is taken into account by using the superpotential formalism. The confinement/deconfinement first order phase transition leads to a gravitational wave stochastic background which mainly depends on the scale mKK and the number of colors, N, in the dual theory. Its power spectrum peaks at a frequency that depends on the amount of tuning required in the electroweak sector. It turns out that the present and forthcoming gravitational wave observatories can probe scenarios where the KK resonances are very heavy. Current aLIGO data already rule out vector boson KK resonances with masses in the interval mKK ∼ ð1–10Þ × 105 TeV. Future gravitational experiments will be sensitive to resonances with masses mKK ≲ 105 TeV (LISA), 108 TeV (aLIGO Design) and 109 TeV (ET). Finally, we also find that the big bang nucleosynthesis bound in the frequency spectrum turns into a lower bound for the nucleation temperature as Tn ≳ 10−4n, Spanish MINEICO FIS2017-85053-C2-1-P FPA2017-88915-P, FEDER/Junta de Andalucia-Consejeria de Economia y Conocimiento 2014-2020 Operational Programme A-FQM-178-UGR18, Junta de Andalucia FQM-225, European Union (EU) SOMM17/6105/UGR, German Research Foundation (DFG) RYC-2016-20678, Catalan Government 2017SGR1069, evero Ochoa Excellence Program of MINEICO SEV2016-0588

We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a non-vanishing instanton superpotential. These show that non-vanishing instanton superpotentials are rare and require a specific pattern for the bundle construction. For the class of monad and extension bundles with this pattern, we derive a sufficient criterion for non-vanishing instanton superpotentials based on an affine Hilbert function. This criterion shows that a non-zero instanton superpotential is common within this class. The criterion can be checked using commutative algebra methods only and depends on the topological data defining the Calabi-Yau X and the vector bundle V., Comment: 21 pages, 7 figures

We find exact finite temperature solutions to $d=5$ Einstein-dilaton gravity with black branes and a Randall--Sundrum 3-brane. We show that there exists a unique generating superpotential for these models. The location of the black brane and the associated Hawking temperature depend on the value of the the 3-brane tension while other parameters are held fixed. The thermodynamics of these solutions are presented, from which we show that the entropy satisfies $S, Comment: 14 pages, 5 figures

Within the superfield formalism, we study the renormalization group improvement of the effective superpotential for the ${\cal N}=2$ Chern-Simons-matter theory, explicitly obtain the improved effective potential and discuss the minima of the effective potential and a problem of mass generation in the theory., Comment: 14 pages, version accepted to PRD

We construct a solvable deformation of two-dimensional theories with (2, 2) supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric and equivalent to TT¯ after using conservation laws. As illustrative examples, we deform theories involving a single (2, 2) chiral superfield. We show that the deformed free theory is on-shell equivalent to the (2, 2) Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in the physical potential which modify the vacuum structure. This suggests that irrelevant deformations of TT¯ type might also affect infrared physics.

We study the modulus stabilization in an ${A}_{4}$ model whose ${A}_{4}$ flavor symmetry is originated from the ${S}_{4}$ modular symmetry. We can stabilize the modulus so that the ${A}_{4}$ invariant superpotential leads to the realistic lepton masses and mixing angles. We also discuss the phenomenological aspect of the present model as a consequence of the modulus stabilization.

We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the Quasi-Steady State (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behaviour of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model., 27 pages, minor clarifications added, typos corrected, revised version to appear in Phys. Rev. D

We consider a cosmological inflation scenario based on a no-scale supergravity sector with $U(1{)}_{R}$ symmetry. It is shown that a tree level $U(1{)}_{R}$ symmetric superpotential alone does not lead to a slowly rolling scalar potential. A deformation of this tree level superpotential by including an explicit $R$ symmetry breaking term beyond the renormalizable level is proposed. The resulting potential is found to be similar (but not exactly the same) to the one in the Starobinsky inflation model. We emphasize that for successful inflation, with the scalar spectral index ${n}_{s}\ensuremath{\sim}0.96$ and the tensor-to-scalar ratio $rl0.08$, a correlation between the mass parameters in the superpotential and the vacuum expectation value of the modulus field $T$ in the K\"ahler potential must be adopted.

Consistency of trans-unification renormalization group (RG) evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10)GUT (NMSGUT). We define the 1-loop RGE β functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) β functions involving large irreps. Use of the RGEs identifies a perturbative domain Q

We study the four-dimensional (4D) scalar potential arising from a generalized type IIA flux superpotential including the (non-)geometric fluxes. First, we show that using a set of peculiar flux combinations, the 4D scalar potential can be formulated into a very compact form. This is what we call as the `symplectic formulation' from which one could easily anticipate the ten-dimensional origin of the effective scalar potential. We support our formulation through an alternate derivation of the scalar potential via considering the Double Field Theory (DFT) reduction on a generic Calabi Yau orientifold. In addition, we also exemplify the insights of our formulation with explicit computations for two concrete toroidal examples using orientifolds of the complex threefolds ${\mathbb T}^6/{({\mathbb Z}_2 \times {\mathbb Z}_2)}$ and ${\mathbb T}^6/{\mathbb Z}_4$., Comment: v4: 33 pages, typos fixed in eqn. (4.22) and (4.23), and some cosmetic changes in the title; version to appear in PRD

We consider higher derivative supergravities that are dual to ghost-free $N=1$ supergravity theories in the Einstein frame. The duality is implemented by deforming the K\"ahler function, and/or the superpotential, to include nonlinear dependences on chiral fields that in other approaches play the role of the Lagrange multipliers employed to establish this duality. These models are of the no-scale type, and in the minimal case, require the presence of four chiral multiplets, with a K\"ahler potential having the structure of the $ SU(4,1)/SU(4) \times U(1) $ coset manifold. In the standard $N=1$ supergravity formulation, these models are described by a multifield scalar potential, featuring Starobinsky-like behavior in particular directions., Comment: 32 pages, 2 figures, pdfLateX, Title slightly changed, text added, references added and corrected, typos corrected, unnecessary figures removed, results unchanged

In the context of studying the 4D effective potentials of type IIB non-geometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level non-geometric scalar potential arising from a flux superpotential which includes the S-dual pairs of non-geometric fluxes $(Q, P)$, the standard NS-NS and RR three-form fluxes $(F_3, H_3)$ and the geometric flux ($\omega$). This `symplectic formulation' is valid for arbitrary numbers of Kahler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as hodge numbers and the triple intersection numbers) of the compactifying (CY) threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kahler- and super-potentials.

In this paper we study the Nielsen identity for the supersymmetric Chern-Simons-matter model in the superfield formalism, in three spacetime dimensions. The Nielsen identity is essential to understand the gauge invariance of the symmetry breaking mechanism, and it is calculated by using the BRST invariance of the model. We discuss the technical difficulties in applying this identity to the complete effective superpotential, but we show how we can study in detail the gauge independence of one part of the effective superpotential, $K_{eff}$. We calculate the renormalization group functions of the model for arbitrary gauge-fixing parameter, finding them to be independent of the gauge choice. This result can be used to argue that $K_{eff}$ also does not depend on the gauge parameter. We discuss the possibility of the extension of these results to the complete effective superpotential.

We present a unified explanation for the $B$-decay anomalies in ${R}_{{D}^{(*)}}$ and ${R}_{K}$ together with the anomalous muon magnetic moment, consistent with the constraints from the current measurements of leptonic decay rates and ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$, ${B}_{s}^{0}\ensuremath{-}{\overline{B}}_{s}^{0}$ mixings, within the framework of a minimal left-right symmetric gauge theory motivated by one of the low-energy subgroups of ${E}_{6}$ naturally accommodating leptoquarks.

In supersymmetric models with radiatively-driven naturalness, higgsino-like electroweak-inos (EW-inos) are expected to lie in a mass range 100--300 GeV, the lighter the more natural. Such states can be pair-produced at high rates at ILC where their masses are nearly equal to the value of the superpotential mu parameter while their mass splittings depend on the gaugino masses M_1 and M_2. The gaugino masses in turn depend on trilinear soft terms---the A parameters, which are expected to lie in the multi-TeV range owing to the 125 GeV Higgs mass---via two-loop contributions to renormalization group running. We examine the extent to which ILC is sensitive to large A-terms via precision EW-ino mass measurement. Extraction of gaugino masses at the percent level should allow for interesting probes of large trilinear soft SUSY breaking terms under the assumption of unified gaugino masses., Comment: 14 pages; 10 .png figures

A scenario of moduli stabilisation based on the interplay between closed and open string sectors is explored in a bottom-up approach. We study N=1 effective supergravities inspired by type IIB orientifold constructions that include background fluxes and non-perturbative effects. The former generate the standard flux superpotential for the axiodilaton and complex structure moduli. The latter can be induced by gaugino condensation in a non-Abelian sector of D7-branes and involve the overall Kaehler modulus of the compactification as well as matter fields. We analyse the dynamics of this coupled system and show that it is compatible with single-step moduli stabilisation in a metastable de Sitter vacuum. A novelty of the scenario is that the F-term potential suffices to generate a positive cosmological constant and to stabilise all moduli, except for a flat direction that can be either lifted by a mass term or eaten up by an anomalous U(1)., 7 pages, 1 figure and 2 tables; v2: Published version

We present the explicit de Sitter supergravity action describing the interaction of supergravity with an arbitrary number of chiral and vector multiplets as well as one nilpotent chiral multiplet. The action has a non-Gaussian dependence on the auxiliary field of the nilpotent multiplet, however, it can be integrated out for an arbitrary matter-coupled supergravity. The general supergravity action with a given Kahler potential $K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent chiral multiplet consists of the standard supergravity action defined by $K$, $W$ and $f_{AB}$ where the scalar in the nilpotent multiplet has to be replaced by a bilinear combination of the fermion in the nilpotent multiplet divided by the Gaussian value of the auxiliary field. All additional contributions to the action start with terms quartic and higher order in the fermion of the nilpotent multiplet. These are given by a simple universal closed form expression., Comment: 15 pages

Super Feynman rules for any superspin are given for massive $ \mathcal{N}=1 $ supersymmetric theories, including momentum superspace on-shell legs. This is done by extending, from space to superspace, Weinberg's perturbative approach to quantum field theory. Superfields work just as a device that allow one to write super Poincare-covariant superamplitudes for interacting theories, relying neither in path integral nor canonical formulations. Explicit transformation laws for particle states under finite supersymmetric transformations are offered. $ \mathit{C}, \mathit{P}, \mathit{T}, $ and $ \mathcal{R} $ transformations are also worked out. A key feature of this formalism is that it does not require the introduction of auxiliary fields, and when introduced, their purpose is just to render supersymmetric invariant the time-ordered products in the Dyson series. The formalism is tested for the cubic scalar superpotential. It is found that when a superparticle is its own antisuperparticle the lowest-order correction of time-ordered products, together with its covariant part, corresponds to the Wess-Zumino model potential.

The Supersymmetric Custodial Triplet Model (SCTM) adds to the particle content of the MSSM three $SU(2)_L$ triplet chiral superfields with hypercharge $Y=(0,\pm1)$. At the superpotential level the model respects a global $SU(2)_L \otimes SU(2)_R$ symmetry only broken by the Yukawa interactions. The pattern of vacuum expectation values of the neutral doublet and triplet scalar fields depends on the symmetry pattern of the Higgs soft breaking masses. We study the cases where this symmetry is maintained in the Higgs sector, and when it is broken only by the two doublets attaining different vacuum expectation values. In the former case, the symmetry is spontaneously broken down to the vectorial subgroup $SU(2)_V$ and the $\rho$ parameter is protected by the custodial symmetry. However in both situations the $\rho$ parameter is protected at tree level, allowing for light triplet scalars with large vacuum expectation values. We find that over a large range of parameter space, a light neutralino can supply the correct relic abundance of dark matter either through resonant s-channel triplet scalar funnels or well tempering of the Bino with the triplet fermions. Direct detection experiments have trouble probing these model points because the custodial symmetry suppresses the coupling of the neutralino and the $Z$ and a small Higgsino component of the neutralino suppresses the coupling with the Higgs. Likewise the annihilation cross sections for indirect detection lie below the Fermi-LAT upper bounds for the different channels., Comment: 26 pages, 8 figures; v2 revised comments on classification method and indirect detection section. Results unchanged, matches PRD published version

We provide type IIB string embeddings of two axion variants of natural inflation. We use a combination of RR 2 form axions as the inflaton field and have its potential generated by non perturbative effects in the superpotential. Besides giving rise to inflation, the models developed take into account the stabilization of the compact space, both in the KKLT and large volume scenario regimes, an essential condition for any semi-realistic model of string inflation., Comment: LaTeX, 1+26 pages, 2 figures; v2: added refs; v3: corrected a LaTeX problem, where v2 refs were compiled with v1 tex file

Using the worldline $SU(2|1)$ superfield approach, we construct $\mathcal{N}=4$ superconformally invariant actions for the $d=1$ multiplets ($\mathbf{1},\mathbf{4},\mathbf{3}$) and ($\mathbf{2},\mathbf{4},\mathbf{2}$). The $SU(2|1)$ superfield framework automatically implies the trigonometric realization of the superconformal symmetry and the harmonic oscillator term in the corresponding component actions. We deal with the general $\mathcal{N}=4$ superconformal algebra $D(2,1;\ensuremath{\alpha})$ and its central-extended $\ensuremath{\alpha}=0$ and $\ensuremath{\alpha}=\ensuremath{-}1$ $psu(1,1|2)\ensuremath{\bigoplus}su(2)$ descendants. We capitalize on the observation that $D(2,1;\ensuremath{\alpha})$ at $\ensuremath{\alpha}\ensuremath{\ne}0$ can be treated as a closure of its two $su(2|1)$ subalgebras, one of which defines the superisometry of the $SU(2|1)$ superspace, while the other is related to the first one through the reflection of $\ensuremath{\mu}$, the parameter of contraction to the flat $\mathcal{N}=4,d=1$ superspace. This closure property and its $\ensuremath{\alpha}=0$ analog suggest a simple criterion for the $SU(2|1)$ invariant actions to be superconformal: they should be even functions of $\ensuremath{\mu}$. We find that the superconformal actions of the multiplet ($\mathbf{2},\mathbf{4},\mathbf{2}$) exist only at $\ensuremath{\alpha}=\ensuremath{-}1,0$ and are reduced to a sum of the free sigma-model-type action and the conformal superpotential yielding, respectively, the oscillator potential $\ensuremath{\sim}{\ensuremath{\mu}}^{2}$ and the standard conformal inverse-square potential in the bosonic sector. The sigma-model action in this case can be constructed only on account of nonzero central charge in the superalgebra $su(1,1|2)$.

While LHC8 Higgs mass and sparticle search constraints favor a multi-TeV value of gravitino mass m_{3/2}, electroweak naturalness favors a superpotential higgsino mass \mu ~100-200 GeV: the mis-match results in an apparent Little Hierarchy characterized by \mu 2m({\rm higgsino}).

We construct the supergravity duals of marginal deformations of a (0,2) Landau-Ginsburg theory that describes the supersymmetric lowest Landau level. These deformations preserve supersymmetry and it is proposed that they are associated with the introduction of a phase in the (0,2) superpotential. We also consider marginal deformations of various field theories that exhibit Schrodinger symmetry and Lifshitz scaling. This includes countably-infinite examples with dynamical exponent z=2 based on the Sasaki-Einstein spaces Y^{p,q} and L^{p,q,r}, as well as an example with general dynamical exponent z >= 1., 20 pages, no figures, corrections and comments added

Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of "Yukawon" Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $\bf{210 \oplus {\overline{126}}\oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $\bf{\overline{126},10}$($\mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $\mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $\bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $\phi,S $, of which the latter's singlet part $S_s$ breaks supersymmetry and the traceless part $\hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.

We present a new paradigm for supersymmetric theories with R-parity violation (RPV). At high scale, R-parity is conserved in the visible sector but spontaneously broken in the SUSY-breaking sector. The breaking is then dynamically mediated to the visible sector and is manifested via non-renormalizable operators at low energy. Consequently, RPV operators originate from the Kahler potential rather than the superpotential, and are naturally suppressed by the SUSY-breaking scale, explaining their small magnitudes. A new set of non-holomorphic RPV operators are identified and found to often dominate over the standard RPV ones. We study the relevant low-energy constraints arising from baryon-number violating processes, proton decay and flavor changing neutral currents, which may all be satisfied if a solution to the Standard Model flavor puzzle is incorporated. The chiral structure of the RPV operators imply new and distinct collider signatures, indicating the need to alter current techniques in searching for RPV at the LHC., 6 pages, 3 figures

In supersymmetric theories, the $R$ symmetry plays a unique role in suppressing a constant term in the superpotential. In single chiral field models of spontaneous breaking of a discrete $R$ symmetry, an $R$-breaking field can be a good candidate for an inflaton in new inflation models. In this paper, we revisit the compatibility of the single-field $R$-breaking new inflation model with the results of the Planck experiment. As a result, we find that the model predicts a lower limit on the gravitino mass, ${m}_{3/2}gO(100)\text{ }\text{ }\mathrm{TeV}$, assuming that the $R$-symmetry breaking is dominantly induced by the inflaton and the inflaton dynamics is not affected by the supersymmetry-breaking sector, which can be guaranteed by symmetry or compositeness of the supersymmetry-breaking sector. This lower limit is consistent with the observed Higgs mass of 126 GeV when the masses of the top squarks are of order the gravitino mass scale. We also show that the baryon asymmetry of the Universe as well as the observed dark matter density can be consistently explained along with the $R$-breaking new inflation model, assuming leptogenesis and that the wino is the lightest supersymmetric particle.

We give the general form of supersymmetric backgrounds with two real supercharges of M-theory and type IIA supergravity (with non-zero Romans mass in general) of the form $\mathbb{R}^{1,d} \times \M_8$, d=1,2, on eight-dimensional manifolds with SU(4) structure. We point out a subtlety in the integrability theorems for low-dimensional supersymmetric compactifications. As a special case we examine Calabi-Yau flux vacua and we show that unbroken supersymmetry does not in general require the four-form flux to be (2,2) or primitive. Our results could be used to construct novel higher-dimensional analogues of the Klebanov-Strassler geometry. In the case of M-theory large-volume Calabi-Yau flux vacua our results are in agreement with partial supersymmetry breaking in three-dimensional N=2 supergravity. Alternatively, the conditions for supersymmetry can be expressed in terms of a real `superpotential' in accordance with three-dimensional N=1 supergravity. We present explicit examples of M-theory flux vacua on K3 \times K3, which however do not appear to possess F-theory duals with four-dimensional Poincare invariance.

We obtain a class of asymptotic flat or (A)dS hairy black holes in D-dimensional Einstein gravity coupled to a scalar with certain scalar potential. For a given mass, the theory admits both the Schwarzschild-Tangherlini and the hairy black holes with different temperature and entropy, but satisfying the same first law of thermodynamics. For some appropriate choice of parameters, the scalar potential can be expressed in terms of a super-potential and it can arise in gauged supergravities. In this case, the solutions develop a naked curvature singularity and become the spherical domain walls. Uplifting the solutions to D=11 or 10, we obtain solutions that can be viewed as spherical M-branes or D3-branes. We also add electric charges to these hairy black holes. All these solutions contain no scalar charges in that the first law of thermodynamics are unmodified. We also try to construct new AdS black holes carrying scalar charges, with some moderate success in that the charges are pre-fixed in the theory instead of being some continuous integration constants., Comment: Latex, 21 pages, references and new comments added, typos corrected. To appear in PRD

In the standard model the proton is protected from decay naturally by gauge symmetries, whereas in the ordinary minimal supersymmetric standard model an ad hoc discrete symmetry is imposed for the proton stability. We present a new supersymmetric model in which the proton decay is forbidden by an extra U(1) gauge symmetry. Particle contents are necessarily increased to be free from anomalies, incorporating right-handed neutrinos. Both Dirac and Majorana masses are generated for neutrinos, yielding nonvanishing but small masses. The superpotential consists only of trilinear couplings and the mass parameter $\ensuremath{\mu}$ of the minimal model is induced by spontaneous breaking of the U(1) symmetry.

The supersymmetric WKB (SWKB) approximation is known to give exact results for translationally shape-invariant potentials. To examine how this approximation fares for potentials which are not shape invariant, we investigate two such potentials: the double oscillator well and the finite square well. In the case of the double oscillator, where the energy levels are nearly degenerate, no analytic expression for the superpotential is possible and the SWKB approximation is far worse than the WKB approximation. But for the finite square well, where the energy spectrum is nondegenerate and an analytic expression for the superpotential is possible, the SWKB approximation is much better than the WKB approximation for almost all states. Thus the discreteness of the energy spectrum and the existence of an analytic expression for the superpotential are preconditions for applicability of the SWKB approximation.

Keeping N=1 supersymmetry in 4-dimension and in the leading order, we disuss the various orbifold compactifications of M-theory suggested by Horava and Witten on $T^6/Z_3$, $T^6/Z_6$, $T^6/Z_{12}$, and the compactification by keeping singlets under $SU(2)\times U(1)$ symmetry, then the compactification on $S^1/Z_2$. We also discuss the next to leading order K\"ahler potential, superpotential, and gauge kinetic function in the $Z_{12}$ case. In addition, we calculate the SUSY breaking soft terms and find out that the universality of the scalar masses will be violated, but the violation might be very small., Comment: 16 pages, latex, no figures

Renormalizable lepton number violating interactions that break R parity can induce a Majorana mass for neutrinos. Based on this, we show that it is possible to obtain a phenomenologically viable neutrino mass matrix that can accommodate atmospheric neutrino data via {nu}{sub {mu}}-{nu}{sub {tau}} mixing and the solar neutrino data via either the large or small angle MSW effect. We argue that such a mass matrix could result from an approximate discrete symmetry of the superpotential that forbids renormalizable baryon number violating couplings. {copyright} {ital 1998} {ital The American Physical Society}

A perturbative non-renormalization theorem is presented that applies to general supersymmetric theories, including non-renormalizable theories in which the $\int d^2\theta$ integrand is an arbitrary gauge-invariant function $F(\Phi,W)$ of the chiral superfields $\Phi$ and gauge field-strength superfields $W$, and the $\int d^4\theta$-integrand is restricted only by gauge invariance. In the Wilsonian Lagrangian, $F(\Phi,W)$ is unrenormalized except for the one-loop renormalization of the gauge coupling parameter, and Fayet-Iliopoulos terms can be renormalized only by one-loop graphs, which cancel if the sum of the U(1) charges of the chiral superfields vanishes. One consequence of this theorem is that in non-renormalizable as well as renormalizable theories, in the absence of Fayet-Iliopoulos terms supersymmetry will be unbroken to all orders if the bare superpotential has a stationary point., Comment: 13 pages (including title page), no figures. Vanilla LaTeX

Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense that the energy spectrum is real and bounded below. Such theories possess PT invariance, but they are not symmetric under parity reflection or time reversal separately. This broken parity symmetry is manifested in a nonzero value for $$, even if $\delta$ is an even integer. This paper extends this idea to a two-dimensional supersymmetric quantum field theory whose superpotential is ${\cal S}(\phi)=-ig(i\phi)^{1+\delta}$. The resulting quantum field theory exhibits a broken parity symmetry for all $\delta>0$. However, supersymmetry remains unbroken, which is verified by showing that the ground-state energy density vanishes and that the fermion-boson mass ratio is unity., Comment: 20 pages, REVTeX, 11 postscript figures

We analyze the low energy behavior of N=1 supersymmetric gauge theories with an SU(Nc)×SU(Nc) gauge group and a Landau-Ginzburg type superpotential. These theories contain fundamentals transforming under one of the gauge groups as well as bifundamental matter which transforms as a fundamental under each. We obtain the parametrization of the gauge coupling on the Coulomb branch in terms of a hyperelliptic curve. The derivation of this curve involves making use of Seiberg’s duality for supersymmetric QCD as well as the classical constraints for Nf=Nc+1 and the quantum modified constraints for Nf=Nc.

We discuss gauge-mediated models which employ a tree-level mass term in the superpotential. We give explicit composite realizations in which the mass terms are not fundamental. Instead, they arise as effective terms in the superpotential from confining gauge dynamics., Comment: 20 pages, LaTeX, 1 figure

This paper explores the conditions under which modified gravitational theories admit the positive mass. Following Witten's spinor argument, it is argued that a single condition should be imposed upon a gauge connection in the super-covariant derivative. Under this condition, we present a simple formula for the divergence of the Nester tensor in Einstein's gravity with general source. Applying this prescription to the Einstein-scalar system, we find that for a certain class of the gauge connection, a special kind of non-canonical scalar-field theory admits the positivity property in addition to the ordinary canonical scalar-field system. In both cases the scalar potential can be written in terms of a superpotential. In the non-canonical case we obtain the most general "BPS" solutions which preserve at least half of the supersymmetry., 8 pages. v2: minor modifications, to appear in PRD

We consider the possibility of a successful Affleck-Dine mechanism alone the u(c)d(c)d(c) direction in R-parity symmetric extensions of the minimal supersymmetric standard model (MSSM) which contain a gauge singlet superfield phi. Such gauge singlets commonly occur in extensions of the MSSM, for example, in models which seek to account for neutrino masses. We consider a two scalar Affleck-Dine mechanism, with the Rat direction stabilized by a nonrenormalizible superpotential term of the form (lambda/M)phi u(c)d(c)d(c) similar to(lambda/M)phi psi(3), where psi corresponds to the gauge nonsinglet flat direction, We give approximate solutions of the Scalar field equations of motion which describe the evolution of the condensates and show that the final baryon asymmetry in this case is suppressed relative to that expected from the conventional single scalar Affleck-Dine mechanism, based on a superpotential term of the form (lambda/4M)psi(4), by a factor [m(s)/(m(phi)+m(s))](1/2), where m(s), is the soft supersymmetry-breaking scalar mass and m(phi) is the supersymmetric phi mass. It is possible for the model to generate a baryon asymmetry even in the limit of unbroken B-L, so long as the gauge singlet condensate does not decay until after anomalous electroweak B+L violation is out of equilibrium following the electroweak phase transition. This condition is generally satisfied if all Dirac neutrino masses are less than around 10 keV. This class of Affleck-Dine models can, in principle, be experimentally ruled out, for example, by the observation of a Dirac mass for the mu or tau neutrino significantly larger than around 10 keV together with a mostly Higgsino LSP.

We give necessary criteria for $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ supersymmetric theories to be in a smoothly confining phase without chiral symmetry breaking and with a dynamically generated superpotential. Using our general arguments we find all such confining SU and Sp theories with a single gauge group and no tree-level superpotential.

In order to raise the Higgs mass up to 125 GeV and relieve the fine-tuning associated with the heavy s-top mass in the minimal supersymmetric standard model (MSSM), we propose a new singlet extension of the MSSM. In this scenario, the additional Higgs mass is radiatively generated also in a hidden sector, and the effect is tansmitted to the Higgs through a messenger field. The Higgs mass can be efficiently increased by the parameters of the superpotential as in the extra matter scenario, but free from the constraints on extra colored matter fields by the LHC experiments. As a result, the tuning problem can be remarkably mitigated by taking low enough messenger mass (\sim 300 GeV) and mass parameter scales (\sim 500 GeV)., 25 pages, 6 eps figures, published version in Phys. Rev. D

Supersymmetric field theories possess a rich structure in their supercurrent supermultiplets. Some symmetries are manifest in one supercurrent supermultiplet but not in the others; for instance, R-symmetry is manifest in the R-multiplet but not in the Ferrara-Zumino multiplet. Similarly, we argue that dilatation symmetry is manifest in the Virial multiplet (also known as a variant minimal supercurrent supermultiplet in the literature). It reveals that R-symmetry and dilatation symmetry are conceptually independent without further assumptions even though the superconformal symmetry connects the two. We show the structure of the Virial multiplet for general renormalizable supersymmetric field theories in (1+3) dimension to all orders in perturbation theory, and discuss the condition for the dilatation invariance (but not necessarily R-symmetric nor superconformal). We present novel scale invariant trajectories with a nilpotent structure in coupling constants for non-unitary Wess-Zumino models with non-vanishing beta functions, which are, therefore, not superconformal., Comment: 33 pages, v2: Appendix added to clarify that our supersymmetric computation gives gauge invariant B-function, which is crucial to understand the correct condition for conformal invariance, v3: minor corrections, to be published, v4: some numerical factors corrected

Local aspects of singular $F$-theory compactifications for supersymmetric grand unified theory model building are fairly well understood in terms of Higgs bundles and their spectral data. Several global issues remain, however, including a description of $G$-fluxes, which are key to constructing chiral matter and stabilizing moduli, and the global realization of $U(1)$ symmetries that can forbid phenomenologically unfavorable couplings. In this paper, we sharpen our earlier proposal for describing $G$-fluxes and $U(1)$s through a distinguished ``Tate'' divisor. As an application, we give a general discussion of M5-instanton contributions in the presence of $G$-flux and exemplify this in a concrete example, where we comment on the ability of instanton-induced superpotential couplings to stabilize K\"ahler moduli.

We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the lagrangian is invariant under the action of the complexified gauge group $\Gc$. From this point of view the usual $D$-flatness conditions are an artifact of Wess--Zumino gauge. By using a gauge that preserves $\Gc$ invariance we show that every constant matter field configuration that extremizes the superpotential is $\Gc$ gauge-equivalent (in a sense that we make precise) to a unique classical vacuum. This result is used to prove that in the absence of a superpotential the classical moduli space is the algebraic variety described by the set of all holomorphic gauge-invariant polynomials. When a superpotential is present, we show that the classical moduli space is a variety defined by imposing additional relations on the holomorphic polynomials. Many of these points are already contained in the existing literature. The main contribution of the present work is that we give a careful and self-contained treatment of limit points and singularities., Comment: 14 pages, LaTeX (uses revtex.sty)

We develop a superfield approach to the effective potential in the supersymmetric Chern-Simons theory coupled to matter, and, in Landau gauge, calculate the one-loop Kahlerian effective potential and give some qualitative prescriptions for the two-loop one., Comment: 11 pages, version accepted to PRD

The positive potential energy required for inflation spontaneously breaks supersymmetry and in general gives any would-be inflaton an effective mass of order the inflationary Hubble parameter thus ruling it out as an inflaton. In this paper I give simple conditions on the superpotential that eliminate some potential sources for this mass, and derive a form for the Kahler potential that eliminates the rest. This reduces the problem of constructing a model of inflation in supergravity to that of constructing one in global supersymmetry with the extra conditions $W=W_\varphi=\psi=0$ during inflation (where $W$ is the superpotential, the inflaton $\in\varphi$, and $W_\psi\neq0$). I then point out that Kahler potentials of the required form often occur in superstrings and that the target space duality symmetries of superstrings often contain R-parities which would make $W=W_\varphi=0$ automatic for $\psi=0$., Comment: 15 pages, version to be published in Physical Review D, major changes in presentation, minor changes in content

We evaluate the Barr-Zee type two-loop level contribution to the fermion electric and chromo-electric dipole moments with sfermion loop in R-parity violating supersymmetric models. It is found that the Barr-Zee type fermion dipole moment with sfermion loop acts destructively to the currently known fermion loop contribution, and that it has small effect when the mass of squarks or charged sleptons in the loop is larger than or comparable to that of the sneutrinos, but cannot be neglected if the sneutrinos are much heavier than loop sfermions., Comment: 5 pages, 3 figures