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We prove a sharp Schwarz type inequality for the Weierstrass- Enneper representation of the minimal surfaces. It states the following. If $F:\mathbf{D}\to \Sigma$ is a conformal harmonic parameterization of a minimal disk $\Sigma$, where $\mathbf{D}$ is the unit disk and $|\Sigma|=\pi R^2$, then $|F_x(z)|(1-|z|^2)\le R$. If for some $z$ the previous inequality is equality, then the surface is an affine disk, and $F$ is linear up to a M\"obius transformation of the unit disk., Comment: 6 pages

We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations., Comment: 39 pages; to appear in Mathematical Journal of Okayama University

Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur., Comment: v3: final version

We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $AdS_3$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles)., Comment: 57 pages, 15 figures

In this paper, we study the Stokes phenomenon of the cyclotomic Knizhnik-Zamolodchikov equation, and prove that its two types of Stokes matrices satisfy the Yang-Baxter and reflection equations respectively. We then discuss its isomonodromy deformation, and its relations with cyclotomic associators, twists, and quantum symmetric pairs., 16 pages

The sandwiched R\'enyi $\alpha$-divergences of two finite-dimensional quantum states play a distinguished role among the many quantum versions of R\'enyi divergences as the tight quantifiers of the trade-off between the two error probabilities in the strong converse domain of state discrimination. In this paper we show the same for the sandwiched R\'enyi divergences of two normal states on an injective von Neumann algebra, thereby establishing the operational significance of these quantities. Moreover, we show that in this setting, again similarly to the finite-dimensional case, the sandwiched R\'enyi divergences coincide with the regularized measured R\'enyi divergences, another distinctive feature of the former quantities. Our main tool is an approximation theorem (martingale convergence) for the sandwiched R\'enyi divergences, which may be used for the extension of various further results from the finite-dimensional to the von Neumann algebra setting. We also initiate the study of the sandwiched R\'enyi divergences of pairs of states on a $C^*$-algebra, and show that the above operational interpretation, as well as the equality to the regularized measured R\'enyi divergence, holds more generally for pairs of states on a nuclear $C^*$-algebra., Comment: 40 pages. To appear in Annales Henri Poincare

We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $G_2 \times SU(2)$ holonomy. Our derivation starts with an explicit description of the Batalin-Vilkovisky complex associated to the three-form multiplet in the pure spinor superfield formalism. We then determine the $L_\infty$ module structure of the supersymmetry algebra on the component fields. We twist the theory by modifying the differential of the Batalin-Vilkovisky complex to incorporate the action of a scalar supercharge. We find that the resulting free twisted theory is given by the tensor product of the de Rham and Dolbeault complexes of the respective $G_2$ and $SU(2)$ holonomy manifolds as conjectured by Costello., 40 pages, 10 tables

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin, Polyakov, and Zamolodchikov [BPZ84a]. Both exhibit exactly solvable structures in two dimensions. A long-standing question [ItTh87] concerns whether there is a direct link between these structures, that is, whether the Virasoro algebra representations of CFT, the distinctive feature of CFT in two dimensions, can be found within lattice models of statistical mechanics. We give a positive answer to this question for the discrete Gaussian free field and for the Ising model, by connecting the structures of discrete complex analysis in the lattice models with the Virasoro symmetry that is expected to describe their scaling limits. This allows for a tight connection of a number of objects from the lattice model world and the field theory one. In particular, our results link the CFT local fields with lattice local fields introduced in [GHP19] and the probabilistic formulation of the lattice model with the continuum correlation functions. Our construction is a decisive step towards establishing the conjectured correspondence between the correlation functions of the CFT fields and those of the lattice local fields. In particular, together with the upcoming [CHI19], our construction will complete the picture initiated in [HoSm13, Hon12, CHI15], where a number of conjectures relating specific Ising lattice fields and CFT correlations were proven., 48 pages, 14 figures

For any positive integer $n$, let $A_n=\mathbb{C}[t_1,\dots,t_n]$, $W_n=\text{Der}(A_n)$ and $\Delta_n=\text{Span}\{\frac{\partial}{\partial{t_1}},\dots,\frac{\partial}{\partial{t_n}}\}$. Then $(W_n, \Delta_n)$ is a Whittaker pair. A $W_n$-module $M$ on which $\Delta_n$ operates locally finite is called a Whittaker module. We show that each block $\Omega_{\mathbf{a}}^{\widetilde{W}}$ of the category of $(A_n,W_n)$-Whittaker modules with finite dimensional Whittaker vector spaces is equivalent to the category of finite dimensional modules over $L_n$, where $L_n$ is the Lie subalgebra of $W_n$ consisting of vector fields vanishing at the origin. As a corollary, we classify all simple non-singular Whittaker $W_n$-modules with finite dimensional Whittaker vector spaces using $\mathfrak{gl}_n$-modules. We also obtain an analogue of Skryabin's equivalence for the non-singular block $\Omega_{\mathbf{a}}^W$.

We show that the strong CP problem is solved in a large class of compactifications of string theory. The Peccei-Quinn mechanism solves the strong CP problem if the CP-breaking effects of the ultraviolet completion of gravity and of QCD are small compared to the CP-preserving axion potential generated by low-energy QCD instantons. We characterize both classes of effects. To understand quantum gravitational effects, we consider an ensemble of flux compactifications of type IIB string theory on orientifolds of Calabi-Yau hypersurfaces in the geometric regime, taking a simple model of QCD on D7-branes. We show that the D-brane instanton contribution to the neutron electric dipole moment falls exponentially in $N^4$, with $N$ the number of axions. In particular, this contribution is negligible in all models in our ensemble with $N>17$. We interpret this result as a consequence of large $N$ effects in the geometry that create hierarchies in instanton actions and also suppress the ultraviolet cutoff. We also compute the CP breaking due to high-energy instantons in QCD. In the absence of vectorlike pairs, we find contributions to the neutron electric dipole moment that are not excluded, but that could be accessible to future experiments if the scale of supersymmetry breaking is sufficiently low. The existence of vectorlike pairs can lead to a larger dipole moment. Finally, we show that a significant fraction of models are allowed by standard cosmological and astrophysical constraints., Comment: 15 pages, 8 figures, 2 appendices. v2: typo fixed, references added

We compute the stringy $E$-function of the affine cone over a Grassmannian. If the Grassmannian is not a projective space then its cone does not admit a crepant resolution. Nonetheless the stringy $E$-function is sometimes a polynomial and in those cases the cone admits a noncommutative crepant resolution. This raises the question as to whether the existence of a noncommutative crepant resolution implies that the stringy $E$-function is a polynomial., v2: final version, incorporated suggestions of the referee. To appear in Proc. Amerc. Math. Soc

The Kac-Moody correction factor, first studied by Macdonald in the affine case, corrects the failure of an identity found by Macdonald in finite-dimensional root systems in 1972. Subsequntly this factor appeared in several formulas in the affine or Kac-Moody analogue of $p$-adic spherical theory for reductive groups. In this article we view the inverse of this correction factor as a function, prove the convergency and holomorphy of this function on a certain domain., Comment: 22 pages

In this paper, we consider double ramification cycles with orbifold targets. An explicit formula for double ramification cycles with orbifold targets, which is parallel to and generalizes the one known for the smooth case, is provided. Some applications for orbifold Gromov--Witten theory are also included., Comment: 49 pages; typo fixed; overall expression improved; comments are welcome!

In Quantum Field Theory, we discuss the main features of the (non-local) contour gauge which extends the local axial-type gauge used in most approaches. Based on the gluon geometry, we demonstrate that the contour gauge does not suffer from the residual gauge. We discuss the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. Having compared the local and non-local gauges, we again advocate the advantage of the contour gauge use., Comment: 9 pages, 2 figures; typos fixed and explanations added

Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior. The highly constrained gauge theory dynamics is encoded in a one-dimensional Bose--Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields. We investigate global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble. Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string-breaking, and paves the way for simulating more complex higher-dimensional gauge theories on quantum synthetic matter devices., Accepted version, 6+6 pages, 4+5 figures

We define a natural state space and Markov process associated to the stochastic Yang-Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributional connections for which holonomies along sufficiently regular curves (Wilson loop observables) and the action of an associated group of gauge transformations are both well-defined and satisfy good continuity properties. The desired state space is obtained as the corresponding space of orbits under this group action and is shown to be a Polish space when equipped with a natural Hausdorff metric. To construct the Markov process we show that the stochastic Yang-Mills heat flow takes values in our space of connections and use the "DeTurck trick" of introducing a time dependent gauge transformation to show invariance, in law, of the solution under gauge transformations. Our main tool for solving for the Yang-Mills heat flow is the theory of regularity structures and along the way we also develop a "basis-free" framework for applying the theory of regularity structures in the context of vector-valued noise - this provides a conceptual framework for interpreting several previous constructions and we expect this framework to be of independent interest., Comment: 141 pages. Revised according to referee reports. Added figures in Section 3. Accepted for publication in Publ. Math. IH\'ES

Using methods of microlocal analysis, we prove that the regularization of divergent amplitudes stays a pure ultraviolet problem in string-localized field theories, despite the weaker localization. Thus, power counting does not lose its significance as an indicator for renormalizability. It also follows that standard techniques can be used to regularize divergent amplitudes in string-localized field theories., 30 pages

We show how the families Seiberg-Witten invariants of a family of smooth $4$-manifolds can be recovered from the families Bauer-Furuta invariant via a cohomological formula. We use this formula to deduce several properties of the families Seiberg-Witten invariants. We give a formula for the Steenrod squares of the families Seiberg-Witten invariants leading to a series of mod $2$ relations between these invariants and the Chern classes of the spin$^c$ index bundle of the family. As a result we discover a new aspect of the ordinary Seiberg-Witten invariants of a $4$-manifold $X$: they obstruct the existence of certain families of $4$-manifolds with fibres diffeomorphic to $X$. As a concrete geometric application, we shall detect a non-smoothable family of $K3$ surfaces. Our formalism also leads to a simple new proof of the families wall crossing formula. Lastly, we introduce $K$-theoretic Seiberg-Witten invariants and give a formula expressing the Chern character of the $K$-theoretic Seiberg-Witten invariants in terms of the cohomological Seiberg-Witten invariants. This leads to new divisibility properties of the families Seiberg-Witten invariants., 76 pages, accepted version. To appear in J. Topology

A globalized version of a trace formula for the Poisson Sigma Model on the disk is presented by using its formal global picture in the setting of the Batalin-Vilkovisky formalism. This global construction includes the concept of zero modes. Moreover, for the symplectic case of the Poisson Sigma Model with cotangent target, the globalized trace reduces to a symplectic construction which was presented by Grady, Li and Li for 1-dimensional Chern-Simons theory (topological quantum mechanics). In addition, the connection between this formula and the Nest-Tsygan theorem and the Tamarkin-Tsygan theorem is explained., Comment: 42 pages, 12 figures

Ball-end milling cutters are one of the most widely used cutters in the automotive, aerospace, die and machine parts industries. In addition, milling chatter will reduce the surface quality and production efficiency, resulting in noise. It is particularly important to model the cutting force and analyze the flutter stability of ball-end milling cutters. In this paper, a simplified milling force model of ball-end milling cutter with three degrees of freedom was established based on Merchant bevel cutting theory. The model simplified the milling force coefficient. The expressions of instantaneous milling area considering the vibration displacements in X, Y and Z directions were derived. The nonlinear dynamic cutting force model of ball-end milling cutter with three degrees of freedom was established. The nonlinear chatter vibration mechanical model of ball-end milling cutter with three degrees of freedom was established by introducing the time delay term, the stability analysis is carried out by time domain simulation. The proposed models were experimentally verified.

Composite ghost is a common phenomenon that widely exists in dynamic scene image mosaic and significantly affects the naturalness of mosaic. To remove the ghost effectively and produce visually natural mosaic, we propose a novel image mosaic method by jointly identifying composite ghost and eliminating ghost regions without distorting, splitting, and duplicating objects. Specifically, our main contributions are three-fold: First, we propose the motion-aware composite ghost identification to localize the potential composite ghosts in the mosaic region (i.e, overlapping area between two images to be stitched) by detecting the salient-moving objects in two stitched images. Second, we design the object-aware alternative region selection strategy to produce ghostless regions that can replace the localized composite ghosts while avoiding object distortion, object separation, and object repetition. Third, we realize the image interpolation-based composite ghost elimination that can generate natural stitched image by eliminating the composite ghost of the initial blending result with the selected image source. We validate the proposed method on challenging datasets and show that our method outperform the state-of-the-art methods.

In this paper, we consider Einstein-Hilbert gravity in the presence of cosmological constant and non-abelian nonlinear electromagnetic field of Born-Infeld type which is minimally coupled to gravity. First, black brane solution of this model is introduced and then color non-abelian DC conductivity is calculated for this solution by using AdS/CFT duality., Comment: 9 Pages, no figure, references added, minor modifications, accepted by the Indian Journal of Physics

The article deals with the methodology of verification of mechanical and electronic torque gauges. Legislative metrological requirements are set for these gauges and the verification process for these types of gauges is also set. The working standard is used to verify two selected torque gauges and then the suitability of these gauges is assessed. Measurement uncertainties are identified to determine the reliability of the measurement process.

Magnetic monopoles play a central role in various areas of fundamental physics, ranging from electromagnetism to topological states of matter. While their observation is elusive in high-energy physics, monopole sources of artificial gauge fields have been recently identified in synthetic matter. String theory, a potentially unifying framework that encompasses quantum mechanics, promotes the conventional \emph{vector} gauge fields of electrodynamics to \emph{tensor} gauge fields, and predicts the existence of more exotic \emph{tensor monopoles} in 4D space. Here we report on the characterization of a tensor monopole synthesized in a 4D parameter space by the spin degrees of freedom of a single solid-state defect in diamond. Using two complementary methods, we characterize the tensor monopole by measuring its quantized topological charge and its emanating Kalb-Ramond field. By introducing a fictitious external field that breaks chiral symmetry, we further observe an intriguing transition in the spectrum, characterized by spectral rings protected by mirror symmetries. Our work represents the first detection of tensor monopoles in a solid-state system and opens up the possibility of emulating exotic topological structures inspired by string theory., Comment: main: 15 pages, 3 figures + SI: 23 pages, 28 figures

In metric spaces, there are quasi-contraction mappings and Suzuki-contraction mapping, that are generalization of contraction mappings. In this article, we give coincidence point theorems of quasi-contraction mappings and Suzuki-contraction mappings in modular spaces, that are generalizations of fixed point theorem of quasi-contractraction mappings and Suzuki-contraction theorem in modular spaces.

In the processing of titanium alloy, the milling parameters determine the process temperature and force. Increasing the milling temperature and force can affect the quality of the titanium alloy produced. In this study, we developed a multi-feature fusion model for high-quality titanium alloy workpieces. In the milling experiments with different milling parameters, an infrared thermal imager and a three-dimensional dynamometer were used to collect the time-domain signals for temperature near the tip of the milling cutter and the milling force. Based on the experimental data, a multi-feature fusion model was established with the milling temperature, milling force, and metal removal rate as the targeted variables, and the milling parameters as the optimized parameters. Based on the particle swarm optimization algorithm, the optimal milling parameters within the test parameters were resolved using the multi-feature fusion model. The results show that: within the milling parameter range of the experimental design, the optimal solutions for the milling parameters are: milling speed of 22.14 m/min; feed speed of 8.25 mm/min; milling depth of 1.36 mm. The multi-feature fusion model resulted in lower milling temperature and force, and provides theoretical guidance for scientifically designing the parameters for the milling process.

Over the last two decades, motivations for modified gravity have emerged from both theoretical and observational levels. $f(R)$ and Chern-Simons gravity have received more attention as they are the simplest generalization. However, $f(R)$ and Chern-Simons gravity contain only an additional scalar (spin-0) degree of freedom and, as a result, do not include other modes of modified theories of gravity. In contrast, quadratic gravity (also referred to as Stelle gravity) is the most general second-order modification to 4-D general relativity and contains a massive spin-2 mode that is not present in $f(R)$ and Chern-Simons gravity. Using two different physical settings $-$ the gravitational wave energy-flux measured by the detectors and the backreaction of the emitted gravitational radiation on the spacetime of the remnant black hole $-$ we demonstrate that massive spin-2 mode carries more energy than the spin-0 mode. Our analysis shows that the effects are pronounced for intermediate-mass black holes, which are prime targets for LISA., Comment: To appear in Nature Scientific Reports

We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, $\mathbb{Z}_N$ gauge theories, and $U(1)_N$ Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, ${\cal N}=1,$ and ${\cal N}=4$ super Yang-Mills theories., 61 pages, 9 figures. v2: minor changes

We propose a possible modification to the tensionless string model with contact interactions. The proposed model aims to reproduce an expectation value of the non-Abelian Wilson loop in the Yang-Mills theory when integrating out string degrees of freedom with a fixed worldsheet boundary. Lie algebra-valued fields whose dynamics are determined by the topological BF action are introduced on the string worldsheet to reproduce path-ordering along the worldsheet boundary. Without bulk contributions, we show that the model describes the non-Abelian Wilson loop discarding effects of self-interactions. Finally, a reproduction of the Wilson loop with three-point interaction is tested in the case of $SU(2)$, 37 pages, 2 figures

de-Sitter(dS) space allows for a generalized class of vacua, known as $\alpha-$vacua, described by some parameters. The Bunch-Davies (BD) vacua is a point in this parameter space. The cosmological correlation function is mostly discussed in BD vacuum in four dimensions and can be interpreted as $CFT_3$ correlation function of certain operators. However, the correlation function in $\alpha-$vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in $\alpha-$vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the $\alpha-$vacua can be related to three-dimensional CFT correlation functions if we relax the requirement of consistency with OPE limit. Relaxation of consistency with OPE limit can be naturally achieved in momentum space., Comment: v2, Added references and corrected typos

We study the effect of ZZ instantons in c = 1 string theory, and demonstrate that they give rise to non-perturbative corrections to scattering amplitudes that do not saturate unitarity within the closed string sector. Beyond the leading non-perturbative order, logarithmic divergences are canceled between worldsheet diagrams of different topologies, due to the Fischler-Susskind-Polchinski mechanism. We propose that the closed string vacuum in c = 1 string theory is non-perturbatively dual to a state of the matrix quantum mechanics in which all scattering states up to a given energy with no incoming flux from the "other side" of the potential are occupied by free fermions. Under such a proposal, we find detailed agreement of non-perturbative corrections to closed string amplitudes in the worldsheet description and in the dual matrix model., Comment: 28 pages, 10 figures; footnote and references added, typos corrected

Tensionless string theory on AdS3 × S3 × M is explored in the limit that the strings wind the asymptotic boundary a large number of times. Although the worldsheet is usually thought to be localised to the AdS boundary, we argue that the string can actually probe the bulk geometry in this limit. In particular, we show that correlation functions can be expressed in terms of a minimal-area worldsheet propagating in AdS3. We then relate the classical motion of the string to the twistor-like free field description of the tensionless worldsheet theory. Finally, we consider a particular dimensional reduction of AdS3 to AdS2, and show that the effective action of the worldsheet formally resembles the one-dimensional Schwarzian theory of JT gravity with conical defects., Journal of High Energy Physics, ISSN:1126-6708, ISSN:1029-8479

We discuss three manners to implement Lorentz symmetry breaking in a superfield theory formulated within the superfield formalism, that is, deformation of the supersymmetry algebra, introducing of an extra superfield whose components can depend on Lorentz-violating (LV) vectors (tensors), and adding of new terms proportional to LV vectors (tensors) to the superfield action. We illustrate these methodologies with examples of quantum calculations., Comment: Presented at the Ninth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 17-26, 2022, 4 pages, minor corrections

We study SU(5) chiral gauge theories on $R^3\times S^1$. With an unequal number of fundamental and antifundmental matter representations we calculate nontrivial pre-ADS superpotentials generated by composite multi-monopoles. We also point out that the structure of the composite multi-monopoles can be determined simply from the affine Dynkin diagrams of the gauge group and its unbroken subgroup. For the case of one flavor, we find that the superpotential is independent of the composite meson. We show that dynamical 4D SUSY breaking in the simplest chiral SU(5) gauge theory can be demonstrated directly via semi-classical effects on the circle., 28 pages plus 17 pages of appendices

We study global 1- and $(d-2)$-form symmetries for gauge theories based on disconnected gauge groups which include charge conjugation. For pure gauge theories, the 1-form symmetries are shown to be non-invertible. In addition, being the gauge groups disconnected, the theories automatically have a $\mathbb{Z}_2$ global $(d-2)$-form symmetry. We propose String Theory embeddings for gauge theories based on these groups. Remarkably, they all automatically come with twist vortices which break the $(d-2)$-form global symmetry. This is consistent with the conjectured absence of global symmetries in Quantum Gravity., 25 pages, no figures

We examine the role of global topological data associated to choices of holonomy for flat gauge fields in string compactification. Our study begins with perturbative string compactification on compact flat manifolds preserving 8 supercharges in 5 dimensions. By including non-trivial holonomy for Wilson lines in the heterotic string and for the B-field gerbe in the type II string we find worldsheet dualities that relate these backgrounds to other string compactifications. While our simple examples allow for explicit analysis, the concepts and some of the methods extend to a broader class of compactifications and have implications for string dualities, perturbative and otherwise., 65 pages, tikz figures; v2: typos corrected

We use semi-derived Ringel-Hall algebras of quivers with loops to realize the whole quantum Borcherds-Bozec algebras and quantum generalized Kac-Moody algebras., Comment: v2, 12 pages, minor edits, accepted by Proc. AMS

When a dyon encircles an infinitely-long solenoid enclosing uniform electric and magnetic fields, its wave function accumulates a duality-invariant quantum phase, which is topological because it depends on a winding number and is nonlocal because the enclosed fields act on the dyon in regions where these fields vanish. Here, we derive this dyon phase and show how its duality symmetry unifies the Aharonov-Bohm phase with its dual phase. We obtain the energy levels, the two-slit interference shift, and the scattering amplitude associated with the duality-invariant quantum phase. Assuming that the dyon has spin 1/2, we show that this spin does not affect the introduced phase. We argue that a spin 1/2 dyon has electric and magnetic moments, the former being greater than the latter because of the Schwinger-Zwanziger quantisation condition., Comment: v3. Published in The European Physical Journal Plus

Black hole superradiance provides a window into the dynamics of light scalar fields and their interactions close to a rotating black hole. Due to the rotation of the black hole, the amplitude of the scalar field becomes magnified, leading to a "black hole bomb" effect. Recent work has demonstrated that rotating black holes in dynamical Chern-Simons gravity possess unique structures, the "Chern-Simons caps," which may influence the behavior of matter near the black hole. Motivated by the presence of these caps, we study superradiance in dynamical Chern-Simons gravity in the context of a slowly rotating black hole. We find that additional modes are excited and contribute to the superradiance beyond what is expected for a Kerr black hole. Studying the superradiant spectrum of perturbations, we find that the Chern-Simons contributions give rise to small corrections to the angular dependence of the resulting scalar cloud. Finally, we comment on potential observable consequences and future avenues for investigation., Comment: Error in Eq. 51-53 and 69-71 corrected, updated discussion

A new variant of the fluid dynamic gauging technique for determining the thickness of soft fouling layers in situ and in real time is reported. The sideways fluid dynamic gauging (SiDG) device allows measurements to be made shortly after a deposit layer contacts a solution, allowing processes such as swelling to be characterized accurately. Two applications of the device are reported: (i) in cleaning, monitoring the change of thickness of a complex food soil when it is contacted with aqueous solutions at different temperatures, pH and surfactant content, and (ii) in fouling, in determining the thickness, thermal conductivity and strength of deposits generated from whey protein solutions on heated stainless steel substrates. The evolution of fouling resistance for the whey protein deposits indicates that significant aging takes place during the fouling test, which is confirmed by changes in the thermal properties and strength of the deposit layer as measured by the SiDG device.

This work is devoted to the geometric approach to supergravity. More precisely, we interpret $\mathcal{N}=1$, $D=4$ supergravity as a super Cartan geometry which provides a link between supergravity and Yang-Mills theory. To this end, we first review important aspects of the theory of supermanifolds and we establish a link between various different approaches. We then introduce super Cartan geometries using the concept of so-called enriched categories. This, among other things, will enable us to implement anticommutative fermionic fields. We will then also show that non-extended $D=4$ supergravity naturally arises in this framework. Finally, using this gauge-theoretic interpretation as well as the chiral structure of the underlying supersymmetry algebra, we will derive graded analoga of Ashtekar's self-dual variables and interpret them in terms of generalized super Cartan connections. This gives canonical chiral supergravity the structure of a Yang-Mills theory with gauge supergroup similar to the self-dual variables in ordinary first-order Einstein gravity which was first observed by F\"ul\"op \cite{Fulop:1993wi}. We then construct the parallel transport map corresponding to the super connection in mathematical rigorous way using again enriched categories. This provides the possibility of quantizing gravity and matter degrees of freedom in loop quantum gravity in a unified way., Comment: v2: equivalence proof extended in section 2.1, typos corrected, references added, 56 pages

We perform imaging of a fundamental string from string scattering amplitudes, and show that its image is a double slit., Comment: 19 pages, 10 figures

We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that this generalized hypergeometric function is a limiting form of the rarefied elliptic hypergeometric function $V^{(r)}$ and derive its transformation properties and a mixed difference-recurrence equation satisfied by it. At the intermediate level we describe symmetries of a more general rarefied hyperbolic hypergeometric function. An important $r=2$ case corresponds to the supersymmetric hypergeometric function given by the integral appearing in the fusion matrix of $N=1$ super Liouville field theory and the Racah-Wigner symbols of the quantum algebra ${\rm U}_q({\rm osp}(1|2))$. We indicate relations to the standard Regge symmetry and prove some previous conjectures for the supersymmetric Racah-Wigner symbols by establishing their different parametrizations., 29 pages

Strongly interacting massive particles are viable dark matter candidates. We consider a dark $Sp(4)$ gauge theory with $N_f=2$ fermions in the pseudo-real fundamental representation and construct the chiral low-energy effective theory. We determine the flavor multiplet structure and the chiral Lagrangian, including the Wess-Zumino-Witten term for mass-degenerate and non-degenerate flavors. We then study the possible charge assignments under a $U(1)'$ gauge symmetry, emphasizing on dark state stability, and provide the full Lagrangian description for Goldstone bosons and vector resonances, including the Wess-Zumino-Witten term. Finally, we use dedicated lattice simulations to determine the chiral low-energy effective theory's validity and low-energy constants. This work represents a self-consistent study of this non-Abelian theory. It thereby provides a framework for future phenomenological exploration in connection to the dark matter problem., Comment: 60 pages, 12 figures; v2: added section 5.4 on eta' meson in the non-degenerate case, minor changes, added references

We extend the work of Schwarz [1] to show that bound states of type IIB supersymmetric ($p, q$)-strings on a circle are associated with M2-branes irreducibly wrapped on $T^2$, or equivalently with nontrivial worldvolume fluxes. Beyond this extension we consider the Hamiltonian of an M2-brane with $C_{\pm}$ fluxes formulated on a symplectic torus bundle with monodromy. In particular, we analyze the relevant case when the monodromy is parabolic. We show that the Hamiltonian is defined in terms of the coinvariant module. We also find that the mass operator is invariant under transformations between inequivalent coinvariants. These coinvariants classify the inequivalent classes of twisted torus bundles with nontrivial monodromy for a given flux. We obtain their associated ($p,q$)-strings via double dimensional reduction, which are invariant under a parabolic subgroup of $SL(2,\mathbb{Q})$. This is the origin of the gauge symmetry of the associated gauged supergravity. These bound states could also be related to the parabolic Scherk-Schwarz reductions of type IIB string theory., 34 pages, 2 Apendices. Improvements were made in the introduction and during the manuscript

The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of supersymmetric string vacua in the desert region and show that even though heuristically the species scale is compatible with expectations, the BPS states of the actual string vacua lead to a stronger dependence of the cutoff scale on the number of massless modes. We propose that this discrepancy, which can be captured by the "BPS desert conjecture", resurrects the idea of a uniform bound on the number of light modes as a way to avoid the black hole species problem. This conjecture also implies a stronger form of the Tadpole Conjecture, which leads to an obstruction in stabilizing all moduli semi-classically for large number of moduli in flux compactifications., Comment: 24 pages + references, 3 figures

An action for a prospect of a $p$-adic open superstring on a target Minkowski space is proposed. The action is constructed for `worldsheet' fields taking values in the $p$-adic field $\mathbb{Q}_p$, but it is assumed to be obtained from a discrete action on the Bruhat-Tits tree. This action is proven to have an analog of worldsheet supersymmetry and the superspace action is also constructed in terms of superfields. The action does not have conformal symmetry, however it is implemented in the definition of the amplitudes. The tree-level amplitudes for this theory are obtained for $N$ vertex operators corresponding to tachyon superfields and a Koba-Nielsen formula is obtained. Finally, four-point amplitudes are computed explicitly and they are compared to previous work on $p$-adic superstring amplitudes., 26 pages, no figures

In this note we present a solution of $N=4,d=7$ gauged supergravity which is holographically dual to a co-dimension two defect living in a six dimensional SCFT. The solution is obtained by double analytic continuation of a two charge supersymmetric black hole solution. The condition that no conical deficits are present in the bulk and on the boundary is satisfied by a one parameter family of solutions for which some holographic observables are computed., 17 pages, PDFLaTeX, 2 figures, v2 reference added

String functions are important building blocks of characters of integrable highest modules over affine Kac--Moody algebras. Kac and Peterson computed string functions for affine Lie algebras of type $A_{1}^{(1)}$ in terms of Dedekind eta functions. We produce new relations between string functions by writing them as double-sums and then using certain symmetry relations. We evaluate the series using special double-sum formulas that express Hecke-type double-sums in terms of Appell--Lerch functions and theta functions, where we point out that Appell--Lerch functions are the building blocks of Ramanujan's classical mock theta functions., 24 pages

In this work, we present the possible existence of a thermalon phase transition between anti-de Sitter (AdS) to de Sitter (dS) vacua in Einstein-Gauss-Bonnet gravity by considering the R\'{e}nyi statistics. A thermalon changes the asymptotic structure of spacetimes via the bubble nucleation of spherical thin-shells which host a black hole in the interior. All relevant thermodynamical quantities are computed in terms of the Renyi statistics in order to demonstrate the possible existence of the AdS to dS phase transition. In addition, we also comment on the behaviors of the phase transitions in the Renyi statistics., Comment: v2: version accepted for publication in Nucl. Phys. B