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The D-term inflation in supergravity, in the braneworld Randall Sundrum II (RSII) context, has been proposed to solve some problems related to the four-dimensional inflation model. That scenario is based on a modification of the Friedmann equation by the addition of the fifth dimension, which corresponds to an energy, called brane tension λ. Therefore, we propose the investigation of the brane effect on the reheating epoch. In this context, we have analyzed the process of reheating and focused on the variation of the temperature value Tre. We found that it depends on all parameters, and the value found is in the range Tre ∼ (7.5 × 108−8 × 1010) GeV, which is consistent with the thermal leptogenesis (Tre ≥ 108 GeV).

Cosmic inflation driven by the vacuum energy associated with the $D$-term of a supersymmetric abelian gauge group and a possible existence of long-range force mediated by an ultra-light gauge boson $Z^\prime$ are two extreme examples of models based on extra $U(1)$ symmetries. Large vacuum energy sets the scale of inflation while the scales of long-range forces induced by anomaly free extra gauged $U(1)$ symmetries are constrained by neutrino oscillations, binary pulsar timings and invisible neutrino decay. There exists a difference of about 40 orders of magnitude between the scales of these two. Also, gauge couplings associated with the long-range forces are very small compared to the standard model couplings and the one required for inflation. We propose a framework based on clockwork mechanism in which these vastly different scales and associated new physics can coexist without invoking any arbitrarily small or large parameter in the fundamental theory. A chain of $U(1)$ is introduced with characteristic nearest-neighbour interactions. A large $D$-term introduced at one end governs the dynamics of inflation. $Z^\prime$ is localized on the other end of the chain, and it can be massless or can get naturally suppressed mass. The standard model fields can be charged under one of the intermediate $U(1)$ in the chain to give rise to their small effective coupling $g^\prime$ with $Z^\prime$. Constraints on $g^\prime$ and $M_{Z^\prime}$ are discussed in the context of the long-range forces of type $L_\mu - L_\tau$, $L_e - L_\mu$ and $B-L$. These, along with the inflation observables, are used to constraint the parameters of the underlying clockwork model., Comment: 22 pages, 6 captioned figures; Minor changes, Published version

The hadronic form factors of the energy-momentum tensor (EMT) have attracted considerable interest in recent literature. This concerns especially the D-term form factor D(t) with its appealing interpretation in terms of internal forces. With their focus on hadron structure, theoretical studies so far have concentrated mainly on strongly interacting systems with short-range forces. Effects on the EMT due to long-range forces like the electromagnetic interaction have not yet been studied. Electromagnetic forces play a small role in the balance of forces inside the proton, but their long-range nature introduces new features which are not present in systems with short-range forces. We use a simple but consistent classical field theoretical model of the proton to show how the presence of long-range forces alters some notions taken for granted in short-range systems. Our results imply that a more careful definition of the D-term is required when long-range forces are present.

We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.

We analyse the consequences of a new gauge invariant Fayet-Iliopoulos (FI) term proposed recently to a class of inflation models driven by supersymmetry breaking with the inflaton being the superpartner of the goldstino. We first show that charged matter fields can be consistently added with the new term, as well as the standard FI term in supergravity in a K\"ahler frame where the $U(1)$ is not an R-symmetry. We then show that the slow-roll conditions can be easily satisfied with inflation driven by a D-term depending on the two FI parameters. Inflation starts at initial conditions around the maximum of the potential where the $U(1)$ symmetry is restored and stops when the inflaton rolls down to the minimum describing the present phase of our Universe. The resulting tensor-to-scalar ratio of primordial perturbations can be even at observable values in the presence of higher order terms in the K\"ahler potential., Comment: 19 pages, 7 figures

We calculate the gravitational form factors of the excited $N(1535)$ state with the quantum numbers $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ via light cone QCD sum rules (LCSR). To this end, we consider the quark part of the energy-momentum tensor (EMT) current and use the general form of the nucleon's interpolating field as well as the distribution amplitudes (DAs) of $N(1535)$. As both the nucleon and $N(1535)$ couple to the same current, the $N(1535) \rightarrow N$ gravitational transition form factors are entered to the calculations as the main input parameters. First we revisit the transitional gravitational form factors of $N(1535) \rightarrow N$, then extract the values of the form factors of the $N(1535)$ excited state. We observe that the gravitational form factors of $N(1535)$ in terms of $Q^2$ are well described by the multipole fit function. As a byproduct, we also calculate the pressure and energy density at the center of $N(1535)$ and estimate its mechanical radius., 12 Pages, 2 Figures and 3 Tables

We study the Dirac-Born-Infeld (DBI) action with one linear and one non-linear supersymmetry in the presence of a constant Fayet-Iliopoulos (FI) D-term added explicitly or through a deformation of supersymmetry transformations. The linear supersymmetry appears to be spontaneously broken since the D auxiliary field gets a non-vanishing vacuum expectation value and an extra term proportional to the FI parameter involving fermions emerges in the non-linear formulation of the action written recently. However in this note, we show that on-shell this action is equivalent to a standard supersymmetric DBI action ${\it without}$ FI term but with redefined tension, at least up to order of mass-dimension 12 effective interactions., 27 pages; v2: minor corrections

We discuss the possibility that inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry allows to satisfy easily the slow-roll conditions, avoiding the so-called [Formula: see text]-problem, and leads to an interesting class of small field inflation models, characterized by an inflationary plateau around the maximum of the scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum describing the present phase of the Universe. Inflation can be driven by either an [Formula: see text]- or a [Formula: see text]-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a rather small tensor-to-scalar ratio of primordial perturbations.

International audience; The problem of moduli stabilisation is discussed in type IIB/F-theory. Considering a configuration of three intersecting D7 branes with fluxes, it is shown that higher loop effects induce logarithmic corrections to the Kaehler potential which can stabilise Kaehler moduli, in particular the internal volume of the compactification space in 4 dimensions. It is also explained how D-term contributions to the effective potential stabilise the rest of the Kaehler moduli and uplift to de Sitter vacua.

We review a dispersive calculation of the D-term form factor, using unsubtracted $t$-channel dispersion relations for the deeply virtual Compton scattering amplitudes. The $t$-channel unitarity relation is saturated with the contribution of two-pion intermediate states, using the two-pion generalized distributions amplitude for the $\gamma^*\gamma\rightarrow \pi \pi$ subprocess and reconstructing the $\pi\pi\rightarrow N\bar{N}$ subprocess from available information on pion-nucleon partial-wave helicity amplitudes. The dispersion-relation results are discussed in comparison with available model predictions and phenomenological extractions.

We develop an approach based on the light-cone sum rules at the leading order of $\alpha_S$ to calculate the gravitational form factors $A(t)$ and $B(t)$ for the valence quark combinations in nucleon. Within the proposed model, the predictions for the gravitational form factor $D(t)$ ($D$-term contributions) have been presented. Comparison with the experimental data and with the results of different models is discussed., Comment: 10 pages, 8 figures; Typos fixed; the version matches the journal variant

We present a model of exclusive $\phi$-meson lepto-production $ep \to e'p'\phi$ near threshold which features the strangeness gravitational form factors of the proton. We argue that the shape of the differential cross section $d\sigma/dt$ is a sensitive probe of the strangeness D-term of the proton., Comment: 9 pages

International audience; The supersymmetry of the non abelian chiral anomaly is exhibited, up to trivial terms, using descent equations and triangle formulas in the framework of N=1 superspace geometry in four dimensions.

We consider three-dimensional Abelian N = 2 supersymmetric Chern–Simons-matter model with two chiral superfields and study local superspace contributions to low-energy effective action in the matter superfields sector of the theory. Using supergraph technique we compute the effective Kahler potential in the explicit form up to the two-loop approximation.

I discuss the possibility that inflation is driven by supersymmetry breaking, with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry to satisfy the slow-roll conditions, avoiding the so-called &eta, problem, leads to an interesting class of small field inflation models, characterised by an inflationary plateau around the maximum of scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum, describing the present phase of the Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and, in the simplest case, predict a rather small tensor-to-scalar ratio of primordial perturbations. This talk is an extended version of an earlier review (Antoniadis, 2018).

Within the MSSM we propose the chaotic inflationary scenario in which the inflaton field is a combination of sleptons and the Higgs field states evolving along the $D$-term flat direction. In the inflation and postinflation reheating processes, a decisive role is played by the MSSM Yukawa superpotential. The vacuum energy during the inflationary era is mainly from the muonic Yukawa coupling, while the inflaton decay and subsequent reheating process dominantly proceeds due to the strange quark Yukawa term. Because of these, the presented scenario is predictive and the results obtained agree well with cosmological observations. In particular, the scalar spectral index and the tensor-to-scalar ratio are respectively, $n_s\simeq 0.966$ and $r=0.00117$. The reheating temperature is found to be $T_r\simeq 7.2\times 10^7$ GeV., Comment: Matched to Phys. Rev. D version

We study the general deformation of $\mathcal N=2$ supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the $SU(2)$ R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of $\mathcal N=2\to \mathcal N=1$ supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-linearly realised, described by a nilpotent constraint on the deformed $\mathcal N=2$ chiral-chiral superfield. We show that the generic magnetic deformation induces an ordinary FI D-term along the linear supersymmetry via the theta-angle. Moreover, we argue that the resulting action differs on-shell from the standard one (DBI+FI) by fermionic contributions., Comment: 28 pages

We consider ${\cal N}=1$ supersymmetric Born-Infeld actions that have a second non-linear supersymmetry. We focus on the model proposed by Bagger and Galperin and show that the breaking of the second supersymmetry is sourced by the new Fayet-Iliopoulos D-term. Interpreting such an action as the effective theory of a space-filling (anti) D3-brane leads to an expression for the new Fayet-Iliopoulos parameter in terms of the brane tension and $\alpha'$., Comment: 35 pages; v2: comments and references added, to appear on JHEP; v3: minor corrections

We propose a new model of single-field D-term inflation in supergravity, where the inflation is driven by a single modulus field which transforms non-linearly under the U(1) gauge symmetry. One of the notable features of our modulus D-term inflation scenario is that the global U(1) remains unbroken in the vacuum and hence our model is not plagued by the cosmic string problem which can exclude most of the conventional D-term inflation models proposed so far due to the CMB observations., Comment: 15 pages, 5 figures

We show that Calabi–Yau n -folds serve as (partial) moduli spaces for a large class of supersymmetric field theory models, constructed in spacetimes of various dimensions and signatures, and with various numbers of supersymmetry generators.

We consider the six-dimensional hypermultiplet, vector and tensor multiplet models in ( 1 , 0 ) harmonic superspace and discuss the corresponding superfield actions. The actions for free ( 2 , 0 ) tensor multiplet and for interacting vector/tensor multiplet system are constructed. Using the superfield formulation of the hypermultiplet coupled to the vector/tensor system we develop an approach to calculation of the one-loop superfield effective action and find its divergent structure.

We propose a new mechanism of (geometric) moduli stabilisation in type IIB/F-theory four-dimensional compactifications on Calabi-Yau manifolds, in the presence of 7-branes, that does not rely on non-perturbative effects. Complex structure moduli and the axion-dilaton system are stabilised in the standard way, without breaking supersymmetry, using 3-form internal fluxes. K\"ahler class moduli stabilisation utilises perturbative string loop corrections, together with internal magnetic fields along the D7-branes world-volume leading to Fayet-Iliopoulos D-terms in the effective supergravity action. The main ingredient that makes the stabilisation possible at a de Sitter vacuum is the logarithmic dependence of the string loop corrections in the large two-dimensional transverse volume limit of the 7-branes., Comment: 15 pages, 2 figures

In this letter, we will study the Chern-Simons-matter theory in Harmonic superspace. It will be shown that this superspace is well suited to write theories with high amount of supersymmetry. This will be done using harmonic variables. The harmonic superspa...

We construct a supergravity-Maxwell theory with a novel embedding of the Fayet-Iliopoulos D-term, leading to spontaneous supersymmetry breaking. The gauging of the R-symmetry is not required and a gravitino mass is allowed for a generic vacuum. When matter couplings are introduced, an uplift through a positive definite contribution to the scalar potential is obtained. We observe a notable similarity to the $\overline{D3}$ uplift constructions and we give a natural description in terms of constrained multiplets., 23 pages, version 3, new appendix on electric-magnetic duality and updated references

This work deals with form factors of the energy-momentum tensor (EMT) of spin-0 particles and the unknown particle property D-term related to the EMT, and is divided into three parts. The first part explores free, weakly and strongly interacting theories to study EMT form factors with the following findings. (i) The free Klein-Gordon theory predicts for the D-term D = -1. (ii) Even infinitesimally small interactions can drastically impact D. (iii) In strongly interacting theories one can encounter large negative D though notable exceptions exist, which includes Goldstone bosons of chiral symmetry breaking. (iv) Contrary to common belief one cannot arbitrarily add "total derivatives" to the EMT. Rather the EMT must be defined in an unambiguous way. The second part deals with the interpretation of EMT form factors in terms of 3D-densities with following results. (i) The 3D-density formalism is internally consistent. (ii) The description is subject to relativistic corrections which are acceptably small in phenomenologically relevant situations including nucleon and nuclei. (iii) The free field result D=-1 persists when a spin-0 boson is not point-like but "heuristically given some internal structure." The third part investigates the question, whether such "giving of an extended structure" can be implemented dynamically, and has the following insights. (i) We construct a consistent microscopic theory which, in a certain parametric limit, interpolates between extended and point-like solutions. (ii) This theory is exactly solvable which is rare in 3+1 dimensions, admits non-topological solitons of Q-ball-type, and has a Gaussian field amplitude. (iii) The interaction of this theory belongs to a class of logarithmic potentials which were discussed in literature, albeit in different contexts including beyond standard model phenomenology, cosmology, and Higgs physics., 26 pages, 3 figures

Recently proposed exceptional field theories (EFTs) making manifest the duality $E_{n(n)}$ symmetry, first observed as nonlinearly realized symmetries of the maximal $d=3,4,...,9$ supergravity ($n=11-d$) and containing 11D and type IIB supergravity as sectors, were formulated in enlarged spacetimes. In the case of $E_{7(7)}$ EFT such an enlarged spacetime can be identified with the bosonic body of the $d=4$ central charge superspace $\Sigma^{(60|32)}$, the ${\cal N}=8$ $d=4$ superspace completed by 56 additional bosonic coordinates associated to central charges of the maximal $d=4$ supersymmetry algebra. In this paper we show how the hypothesis on the relation of all the known $E_{n(n)}$ EFTs, including $n=8$, with supersymmetry leads to the conjecture on existence of 11D exceptional field theory living in 11D tensorial central charge superspace $\Sigma^{(528|32)}$ and underlying all the $E_{n(n)}$ EFTs with $n=2,...,8$, and probably the double field theory (DFT). We conjecture the possible form of the section conditions of such an 11D EFT and show that quite generic solutions of these can be generated by superparticle models the ground states of which preserve from one half to all but one supersymmetry. The properties of these superparticle models are briefly discussed. We argue that, upon quantization, their quantum states should describe free massless non-conformal higher spin fields in D=11. We also discuss some relevant representations of the M-theory superalgebra which, in the present context, describes supersymmetry of the 11D EFT., Comment: 33 pages. V2: references added. V3: 42 pages. Minor corrections. New sections 3.3 and 5 added. Published in NPB

We propose a new type of supersymmetric Twin Higgs model where the SU(4) invariant quartic term is provided by a D-term potential of a new U(1) gauge symmetry. In the model the 125 GeV Higgs mass can be obtained for stop masses below 1 TeV, and a tuning required to obtain the correct electroweak scale can be as low as 20 %. A stop mass of about 2 TeV is also possible with tuning of order O(10) %., 27 pages, 5 figures; v2: appendix extended, matches version published in JHEP

The supersymmetric extension of “Starobinsky” R + α R 2 models of inflation is particularly simple in the “new minimal” formalism of supergravity, where the inflaton has no scalar superpartners. This paper is devoted to matter couplings in such supergravity models. We show how in the new minimal formalism matter coupling presents certain features absent in other formalisms. In particular, for the large class of matter couplings considered in this paper, matter must possess an R-symmetry, which is gauged by the vector field which becomes dynamical in the “new minimal” completion of the R + α R 2 theory. Thus, in the dual formulation of the theory, where the gauge vector is part of a massive vector multiplet, the inflaton is the superpartner of the massive vector of a nonlinearly realized R-symmetry. The F-term potential of this theory is of no-scale type, while the inflaton potential is given by the D-term of the gauged R-symmetry. The absolute minimum of the potential is always exactly supersymmetric, so in this class of models if realistic vacua exist, they must be always metastable. We also briefly comment on possible generalizations of the examples discussed here and we exhibit some features of higher-curvature supergravity coupled to matter in the “old minimal” formalism.

We revisit the D-term inflation and amend it with ghost-free higher derivative couplings of chiral superfields to super-curvature. These couplings realize a more generic inflationary phase in supergravity. After pointing out that a consistent embedding of these specific higher derivatives is known to exist only in the new-minimal supergravity, we show how a potential for the scalar component may arise due to a Fayet-Iliopoulos D-term. We then turn to inflationary cosmology and explicitly discuss different types of potentials, which capture properties of the common scenarios. These models thanks to the derivative coupling: i) naturally evade the supergravity $\eta$-problem, ii) drive inflation for a wider range of parameter values, and iii) predict lower values for the tensor-to-scalar ratio., Comment: plain text, 12 pages, PLB Journal version

We study a supergravity D-term chaotic inflationary model, in the context of the braneworld scenario, in particular we consider the Randall—Sundrum model type 2. Using the latest release from the combination of WMAP9, eCMB, BAO, and H0, we show that the inflation observables depend only on the number of e-folds N. We also derive all known spectrum inflationary parameters, which are widely consistent with WMAP9 data for a particular choice of values N specially for the scalar spectral index ns and the ratio r. However, the running of the scalar spectral index dns/dlnk is now excluded from the range given by the latest observational measurements.

We study the decoupling limit of a superheavy sgoldstino field in spontaneously broken N=1 supergravity. Our approach is based on K\"ahler superspace, which, among others, allows direct formulation of N=1 supergravity in the Einstein frame and correct identifications of mass parameters. Allowing for a non-renormalizable K\"ahler potential in the hidden sector, the decoupling limit of a superheavy sgoldstino is identified with an infinite negative K\"ahler curvature. Constraints that lead to non-linear realizations of supersymmetry emerge as consequence of the equations of motion of the goldstino superfield when considering the decoupling limit. Finally, by employing superspace Bianchi identities, we identify the real chiral superfield, which will be the superconformal symmetry breaking chiral superfield that enters the conservation of the Ferrra-Zumino multiplet in the field theory limit of N=1 supergravity., Comment: 15 pages, version to be published in Phys. Lett. B

Several topics in the theory of generalized parton distributions (GPDs) are reviewed. First, we give a brief overview of the basics of the theory of generalized parton distributions and their relationship with simpler phenomenological functions, viz. form factors, parton densities and distribution amplitudes. Then, we discuss recent developments in building models for GPDs that are based on the formalism of double distributions (DDs). A special attention is given to a careful analysis of the singularity structure of DDs. The DD formalism is applied to construction of a model GPDs with a singular Regge behavior. Within the developed DD-based approach, we discuss the structure of GPD sum rules. It is shown that separation of DDs into the so-called “plus” part and the D-term part may be treated as a renormalization procedure for the GPD sum rules. This approach is compared with an alternative prescription based on analytic regularization.

Hybrid inflation, driven by a Fayet-Iliopoulos (FI) D term, is an intriguing inflationary model. In its usual formulation, it however suffers from several shortcomings. These pertain to the origin of the FI mass scale, the stability of scalar fields during inflation, gravitational corrections in supergravity, as well as to the latest constraints from the cosmic microwave background. We demonstrate that these issues can be remedied if D-term inflation is realized in the context of strongly coupled supersymmetric gauge theories. We suppose that the D term is generated in consequence of dynamical supersymmetry breaking. Moreover, we assume canonical kinetic terms in the Jordan frame as well as an approximate shift symmetry along the inflaton direction. This provides us with a unified picture of D-term inflation and high-scale supersymmetry breaking. The D term may be associated with a gauged U(1)_B-L, so that the end of inflation spontaneously breaks B-L in the visible sector., Comment: 5 pages + references, 1 figure. v2: slightly extended discussion, updated references, matches version published in PRD

We present a dynamical cosmological solution that simultaneously accounts for the early inflationary stage of the Universe and solves the supersymmetric little hierarchy problem via the relaxion mechanism. First, we consider an inflationary potential arising from the $D$ term of a new $U(1)$ gauge symmetry with a Fayet-Iliopolous term that is independent of the relaxion. A technically natural, small $U(1)$ gauge coupling, $g\ensuremath{\lesssim}{10}^{\ensuremath{-}8}$, allows for a low Hubble scale of inflation, ${H}_{I}\ensuremath{\lesssim}1{0}^{5}\text{ }\text{ }\mathrm{GeV}$, which is shown to be consistent with Planck data. This feature is then used to realize a supersymmetric two-field relaxion mechanism, where the second field is identified as the inflaton provided that ${H}_{I}\ensuremath{\lesssim}10\text{ }\text{ }\mathrm{GeV}$. The inflaton controls the relaxion barrier height allowing the relaxion to evolve in the early Universe and scan the supersymmetric soft masses. After electroweak symmetry is broken, the relaxion settles at a local supersymmetry-breaking minimum with a range of $F$-term values that can naturally explain supersymmetric soft mass scales up to $1{0}^{6}\text{ }\text{ }\mathrm{GeV}$.

We briefly describe a new superextended Landau model with a worldline N=4 supersymmetry and an internal target space ISU (2|2) supersymmetry. It shares many features with the previously studied N=2 supersymmetric Landau model, which is also briefly described.

We study α’-corrections in multiple D7-brane configurations with non-commuting profiles for their transverse position fields. We focus on T-brane systems, crucial in F-theory GUT model building. There α ′ -corrections modify the D-term piece of the BPS equations which, already at leading order, require a non-primitive Abelian worldvolume flux background. We find that α ′ -corrections may either i) leave this flux background invariant, ii) modify the Abelian non-primitive flux profile, or iii) deform it to a non-Abelian profile. The last case typically occurs when primitive fluxes, a necessary ingredient to build 4d chiral models, are added to the system. We illustrate these three cases by solving the α ′ -corrected D-term equations in explicit examples, and describe their appearance in more general T-brane backgrounds. Finally, we discuss implications of our findings for F-theory GUT local models.

In this work we investigate some features of the fermionic sector of the supersymmetric version of the baby Skyrme model. We find that, in the background of BPS compact Skyrmions, fermionic zero modes are confined to the defect core. Further, we show that, while three SUSY generators are broken in the defect core, SUSY is completely restored outside. We study also the effect of a D-term deformation of the model. Such a deformation allows for the existence of fermionic zero modes and broken SUSY outside the compact defect., Comment: Minor corrections. Version to appear in PRD

Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking corrections., 6 pages LaTeX, 9 figures; typos corrected; to be published version

Minimal chaotic models of D-term inflation predicts too large primordial tensor perturbations. Although it can be made consistent with observations utilizing higher order terms in the K\"ahler potential, expansion is not controlled in the absence of symmetries. We comprehensively study the conditions of K\"ahler potential for D-term plateau-type potentials and discuss its symmetry. They include the alpha-attractor model with a massive vector supermultiplet and its generalization leading to pole inflation of arbitrary order. We extend the models so that it can describe Coulomb phase, gauge anomaly is cancelled, and fields other than inflaton are stabilized during inflation. We also point out a generic issue for large-field D-term inflation that the masses of the non-inflaton fields tend to exceed the Planck scale., Comment: 31 pages, 3 figures; version 2, published version, minor revision

Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. This proceeding is a very short summary on the paper [arXiv:1003.0678 [hep-th]], which was done with the collaboration of Carlos R. Mafra.