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Differential $KO$-theory via gradations and mass terms Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-10-12 Kiyonori Gomi, Mayuko Yamashita
We construct models of the differential $KO$-theory and the twisted differential $KO$-theory, by refining Karoubi’s $KO$-theory $\href{https://worldcat.org/title/1120894092}{[Kar78]}$ in terms of gradations on Clifford modules. In order for this, we set up the generalized Clifford superconnection formalism which generalizes the Quillen’s superconnection formalism $\href{https://doi.org/10.1016/004
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JT gravity coupled to fermions Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-10-12 Tom Banks, Patrick Draper, Bingnan Zhang
We argue that two-dimensional dilaton gravity models can all be derived from an analog of Jacobson’s covariant version of the first law of thermodynamics.We then specialize to the JT gravity model and couple it to massless fermions. This model is exactly soluble in quantum field theory, and we present a new derivation of that result. The field theory model violates two principles one might want to
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$3$-manifolds and Vafa–Witten theory Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-10-12 Sergei Gukov, Artan Sheshmani, Shing-Tung Yau
We initiate explicit computations of Vafa–Witten invariants of $3$-manifolds, analogous to Floer groups in the context of Donaldson theory. In particular, we explicitly compute the Vafa–Witten invariants of $3$-manifolds in a family of concrete examples relevant to various surgery operations (the Gluck twist, knot surgeries, log-transforms). We also describe the structural properties that are expected
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Yang–Mills as a constrained Gaussian Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-10-12 Tamer Tlas
Yang–Mills is reformulated in terms of the logarithmic derivative of the holonomies. The classical equations of motion are recovered, and the path integral is rewritten in two ways, both of which are of the form of a Gaussian satisfying a quadratic constraint.
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String condensations in $3+1D$ and Lagrangian algebras Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-10-12 Jiaheng Zhao, Jia-Qi Lou, Zhi-Hao Zhang, Ling-Yan Hung, Liang Kong, Yin Tian
We present three Lagrangian algebras in the modular $2$-category associated to the $3+1D \; \mathbb{Z}^2$ topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps (braided autoequivalences) exchanging algebras with bulk domain walls. A Lagrangian algebra, together with its modules and local modules, encapsulates detailed
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Fractional quantum Hall effect and $M$-theory Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-07-13 Cumrun Vafa
We propose a unifying model for FQHE which on the one hand connects it to recent developments in string theory and on the other hand leads to new predictions for the principal series of experimentally observed FQH systems with filling fraction $\nu=\frac{n}{2n \pm 1}$ as well as those with $\nu=\frac{m}{m+2}$. Our model relates these series to minimal unitary models of the Virasoro and super-Virasoro
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$T \bar{T}$ deformations in general dimensions Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-07-13 Marika Taylor
It has recently been proposed that Zamoldchikov’s $T \bar{T}$ deformation of two-dimensional CFTs describes the holographic theory dual to $\mathrm{AdS}_3$ at finite radius. In this note we use the Gauss–Codazzi form of the Einstein equations to derive a relationship in general dimensions between the trace of the quasi-local stress tensor and a specific quadratic combination of this stress tensor,
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Holographic space-time, Newton’s law, and the dynamics of horizons Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-07-13 Tom Banks, Willy Fischler
We revisit the construction of models of quantum gravity in $d$ dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton’s law. The scattering amplitudes in these models describe scattering of jets
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Algebraic interplay between renormalization and monodromy Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-07-13 Dirk Kreimer, Karen Yeats
We investigate combinatorial and algebraic aspects of the interplay between renormalization and monodromies for Feynman amplitudes. We clarify how extraction of subgraphs from a Feynman graph interacts with putting edges onshell or with contracting them to obtain reduced graphs. Graph by graph this leads to a study of cointeracting bialgebras. One bialgebra comes from extraction of subgraphs and hence
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Crossing symmetry in matter Chern–Simons theories at finite $N$ and $k$ Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-07-13 Umang Mehta, Shiraz Minwalla, Chintan Patel, Shiroman Prakash, Kartik Sharma
We present a conjecture for the crossing symmetry rules for Chern–Simons gauge theories interacting with massive matter in $2 + 1$ dimensions. Our crossing rules are given in terms of the expectation values of particular tangles of Wilson lines, and reduce to the standard rules at large Chern–Simons level. We present completely explicit results for the special case of two fundamental and two antifundamental
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A note on the canonical formalism for gravity Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-07-13 Edward Witten
We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a relationship of the phase space of gravity in asymptotically Anti de Sitter spacetime to a cotangent bundle. We describe what is known about this relationship and some
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Shifted symplectic reduction of derived critical loci Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Mathieu Anel, Damien Calaque
We prove that the derived critical locus of a $G$-invariant function $S : X \to \mathbb{A}^1$ carries a shifted moment map, and that its derived symplectic reduction is the derived critical locus of the induced function $S_{red} : X/G \to \mathbb{A}^1$ on the orbit stack. We also provide a relative version of this result, and show that derived symplectic reduction commutes with derived lagrangian intersections
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Families of Hitchin systems and $N=2$ theories Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Aswin Balasubramanian, Jacques Distler, Ron Donagi
Motivated by the connection to 4d $\mathcal{N} = 2$ theories, we study the global behavior of families of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying curve varies over the Deligne–Mumford moduli space of stable pointed curves. In particular, we describe a flat degeneration of the Hitchin system to a nodal base curve and show that the behaviour of the integrable system at the
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$T$-dual solutions and infinitesimal moduli of the $G_2$-Strominger system Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Andrew Clarke, Mario Garcia-Fernandez, Carl Tipler
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. First studied by Friedrich and Ivanov, the resulting system of partial differential equations describes compactifications of the heterotic string to three dimensions
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Deformations of holomorphic pairs and $2d$-$4d$ wall-crossing Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Veronica Fantini
We show how wall-crossing formulas in coupled $2d$-$4d$ systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a holomorphic vector bundle. The main part of the paper studies the relation between scattering diagrams and deformations of holomorphic pairs, building on recent
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Convergence of eigenstate expectation values with system size Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Yichen Huang
Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a smooth function of energy density as the system size diverges. In translation-invariant quantum lattice systems in any spatial dimension, we prove that for all but
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Integral and differential structures for quantum field theory Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Louis Labuschagne, Adam Majewski
The aim of this work is to firstly demonstrate the efficacy of the recently proposed Orlicz space formalism for Quantum theory [44], and secondly to show how noncommutative differential structures may naturally be incorporated into this framework. To start off with we specifically propose regularity conditions which in the context of local algebras corresponding to Minkowski space, ensure good behaviour
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On the complex affine structures of SYZ-fibration of del Pezzo surfaces Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
Given any smooth cubic curve $E \subseteq \mathbb{P}^2$, we show that the complex affine structure of the special Lagrangian fibration of $\mathbb{P}^2 \: \backslash \: E$ constructed by Collins–Jacob–Lin [12] coincides with the affine structure used in Carl–Pomperla–Siebert [15] for constructing mirror. Moreover, we use the Floer-theoretical gluing method to construct a mirror using immersed Lagrangians
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Gauge fixing and regularity of axially symmetric and axistationary second order perturbations around spherical backgrounds Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-06-30 Marc Mars, Borja Reina, Raül Vera
Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly hard as one needs to understand in depth the process of gauge fixing before attempting any uniqueness proof. This is the first paper of a series of two aimed at deriving
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Sheaves of AQ normal series and supermanifolds Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Kowshik Bettadapura
On a group $G$, a filtration by normal subgroups is referred to as a normal series. If subsequent quotients are abelian, the filtration is referred to as an abelian-quotient normal series, or ‘AQ normal series’ for short. In this article we consider ‘sheaves of AQ normal series’. From a given AQ normal series satisfying an additional hypothesis we derive a complex whose first cohomology obstructs the
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Ramond–Ramond fields and twisted differential K-theory Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Daniel Grady, Hisham Sati
We provide a systematic approach to describing the Ramond–Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new conceptual framework and a mathematically solid setting
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Conformal fields and the structure of the space of solutions of the Einstein constraint equations Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Michael Holst, David Maxwell, Rafe Mazzeo
The drift method, introduced in [22], provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly greater analytic complexity over, say, the conformal or conformal thin sandwich methods. We review this theory here and apply it to the study of solutions of the constraint equations
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General relativity from $p$-adic strings Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 An Huang, Bogdan Stoica, Shing-Tung Yau
For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum $p$-adic strings, similar to the ordinary bosonic strings case. It turns out that spherical vectors of unramified principal series representations of $PGL (2,\mathbb{Q}_p)$
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Asymptotics of the Banana Feynman amplitudes at the large complex structure limit Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Hiroshi Iritani
Recently Bönisch–Fischbach–Klemm–Nega–Safari [3] discovered, via numerical computation, that the leading asymptotics of the $l$-loop Banana Feynman amplitude at the large complex structure limit can be described by the Gamma class of a degree $(1, \dotsc, 1)$ Fano hypersurface $F$ in $(\mathbb{P}^1)^{l+1}$. We confirm this observation by using a Gamma-conjecture type result [10] for $F$.
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Extremal $1/2$ Calabi–Yau $3$-folds and six-dimensional F-theory applications Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Yusuke Kimura
We discuss a method for classifying the singularity types of $1/2$ Calabi–Yau $3$-folds, a family of rational elliptic $3$-folds introduced in a previous study in relation to various U(1) factors in 6D F-theory models. A projective dual pair of del Pezzo manifolds recently studied by Mukai is used to analyze the singularity types. In particular, we studied the maximal rank seven singularity types of
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Extremal isosystolic metrics with multiple bands of crossing geodesics Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Usman Naseer, Barton Zwiebach
We apply recently developed convex programs to find the minimal-area Riemannian metric on $2n$-sided polygons $(n \geq 3)$ with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular $2n$-gon. The hexagon was considered by Calabi. The region covered by the maximal number $n$ of geodesics bands extends
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Heat kernel for the quantum Rabi model Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Cid Reyes-Bustos, Masato Wakayama
The quantum Rabi model (QRM) is widely recognized as a particularly important model in quantum optics and beyond. It is considered to be the simplest and most fundamental system describing quantum light-matter interaction. The objective of the paper is to give an analytical formula of the heat kernel of the Hamiltonian explicitly by infinite series of iterated integrals. The derivation of the formula
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An extension of polar duality of toric varieties and its consequences in Mirror Symmetry Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-03-30 Michele Rossi
The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called framed duality, so giving rise to a powerful and unified method of producing mirror partners of hypersurfaces and complete intersections in toric varieties, of any Kodaira dimension. In particular, the class of projective hypersurfaces and their mirror partners
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Topological recursion for the extended Ooguri–Vafa partition function of colored HOMFLY-PT polynomials of torus knots Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-02-22 Petr Dunin-Barkowski, Maxim Kazarian, Aleksandr Popolitov, Sergey Shadrin, Alexey Sleptsov
We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the $n$-point functions of a particular partition function called the extended Ooguri–Vafa partition function. This generalizes and refines the results of Brini–Eynard–Mariño and Borot–Eynard–Orantin. We also discuss how the statement of spectral curve topological recursion in
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CFTs on curved spaces Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-02-22 Ken Kikuchi
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components of conformal groups acting on various metric spaces using a simple fact; given local coordinate systems be single-valued. Boundary conditions thus obtained which
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On the complex affine structures of SYZ fibration of del Pezzo surfaces Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-02-22 Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
Given any smooth cubic curve $E \subseteq \mathbb{P}^2$, we show that the complex affine structure of the special Lagrangian fibration of $\mathbb{P}^2 \setminus E$ constructed by Collins–Jacob–Lin [12] coincides with the affine structure used in Carl–Pomperla–Siebert [15] for constructing mirror. Moreover, we use the Floer-theoretical gluing method to construct a mirror using immersed Lagrangians
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Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2023-02-22 Hisham Sati, Urs Schreiber
We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that brane charge quantization in this differential $4$-Cohomotopy theory implies intersecting $p \perp (p+2)$-brane moduli given by ordered configurations of points in the transversal $3$-space. Then we show
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Towards super Teichmuller spin TQFT Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-12-27 Nezhla Aghaei, M. K. Pawelkiewicz, Masahito Yamazaki
The quantization of the Teichmüller theory has led to the formulation of the so-called Teichmüller TQFT for $3$‑manifolds. In this paper we initiate the study of “supersymmetrization” of the Teichmüller TQFT, which we call the super Teichmüller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichmüller spin TQFT for a class of spin $3$‑manifold geometries, by taking
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The $\mathsf{CP}^{n-1}$-model with fermions: a new look Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-12-27 Dmitri Bykov
We elaborate the formulation of the $\mathsf{CP}^{n-1}$ sigma model with fermions as a gauged Gross–Neveu model. This approach allows to identify the super phase space of the model as a supersymplectic quotient. Potential chiral gauge anomalies are shown to receive contributions from bosons and fermions alike and are related to properties of this phase space. Along the way we demonstrate that the worldsheet
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$F$-theory over a Fano threefold built from $A_4$-roots Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-12-27 Herbert Clemens, Stuart Raby
In a previous paper, the authors showed the advantages of building a $\mathbb{Z}_2$-action into an $F$-theory model $W_4 / B_3$, namely the action of complex conjugation on the complex algebraic group with compact real form $E_8$. The goal of this paper is to construct the Fano threefold $B_3$ directly from the roots of $SU(5)$ in such a way that the action of complex conjugation is exactly the desired
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Moduli space of stationary vacuum black holes from integrability Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-12-27 James Lucietti, Fred Tomlinson
We consider the classification of asymptotically flat, stationary, vacuum black hole spacetimes in four and five dimensions, that admit one and two commuting axial Killing fields respectively. It is well known that the Einstein equations reduce to a harmonic map on the two-dimensional orbit space, which itself arises as the integrability condition for a linear system of spectral equations. We integrate
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Single-valued hyperlogarithms, correlation functions and closed string amplitudes Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-12-27 Pierre Vanhove, Federico Zerbini
We give new proofs of a global and a local property of the integrals which compute closed string theory amplitudes at genus zero. Both kinds of properties are related to the newborn theory of singlevalued periods, and our proofs provide an intuitive understanding of this relation. The global property, known in physics as the KLT formula, is a factorisation of the closed string integrals into products
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A geometric construction of representations of the Berezin–Toeplitz quantization Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-10-21 Kwokwai Chan, Naichung Conan Leung, Qin Li
For a Kähler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin–Toeplitz deformation quantization algebra $(C^\infty (X) [[\hbar]], \star_{BT})$ parametrized by points $z_0 \in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^0 (X, L^{\otimes m})$ around $z_0$ in the large volume
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On 5D SCFTs and their BPS quivers. Part I: B-branes and brane tilings Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-10-21 Cyril Closset, Michele Del Zotto
We study the spectrum of BPS particles on the Coulomb branch of five-dimensional superconformal field theories (5d SCFTs) compactified on a circle. By engineering these theories in M‑theory on $\mathbf{X} \times S^1$, for $\mathbf{X}$ an isolated Calabi–Yau threefold singularity, we naturally identify the BPS category of the 5d theory on a circle with the derived category of coherent sheaves on a resolution
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Almost contact structures on manifolds with a $G_2$ structure Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-10-21 Xenia de la Ossa, Magdalena Larfors, Matthew Magill
We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a $G_2$ structure. These are of interest for certain supersymmetric configurations in string and M‑theory. We compute the torsion of the $SU(3)$ structure associated to an ACMS and apply these computations to heterotic $G_2$ systems and supersymmetry enhancement. We initiate the study of
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General couplings of four dimensional Maxwell–Klein–Gordon system: Global existence Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-10-21 Mulyanto Mulyanto, Fiki Taufik Akbar, Bobby Eka Gunara
In this paper, we consider the multi component fields interactions of the complex scalar fields and the electromagnetic fields (Maxwell–Klein–Gordon system) on four dimensional Minkowski spacetime with general gauge couplings and the scalar potential turned on. Moreover, the complex scalar fields span an internal manifold assumed to be Kähler. Then, by taking the Kähler potential to be bounded by $U(1)^N$
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Masses, sheets and rigid SCFTs Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-09-14 Aswin Balasubramanian, Jacques Distler
We study mass deformations of certain three-dimensional $\mathcal{N}=4$ Superconformal Field Theories (SCFTs) that have come to be called $T^\rho [G]$ theories. These are associated to tame defects of the six dimensional $(0, 2)$ SCFT $X[\mathfrak{j}]$ for $\mathfrak{j}=A,D,E$. We describe these deformations using a refined version of the theory of sheets, a subject of interest in Geometric Representation
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Distinguished curves and integrability in Riemannian, conformal, and projective geometry Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-09-14 A. Rod Gover, Daniel Snell, Arman Taghavi-Chabert
We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is a type of moving incidence relation. The characterisation is used to provide a very general theory and construction of quantities that are necessarily conserved along the curves. The formalism immediately yields explicit formulae for these
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$\tfrac{1}{2}$Calabi–Yau $4$-folds and four-dimensional F-theory on Calabi–Yau $4$-folds with $\mathrm{U}(1)$ factors Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-09-14 Yusuke Kimura
In this study, four dimensional $N=1$ F‑theory models with multiple $\mathrm{U}(1)$ gauge group factors are constructed. A class of rational elliptic 4‑folds, which we call as “$\tfrac{1}{2}$Calabi–Yau 4‑folds,” is introduced, and we construct the elliptically fibered 4‑folds by utilizing them. This yields a novel approach for building families of elliptically fibered Calabi–Yau 4‑folds with positive
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Lorentz Meets Lipschitz Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-09-14 Christian Lange, Alexander Lytchak, Clemens Sämann
We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $\mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $\alpha$-Hölder
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On gerbe duality and relative Gromov–Witten theory Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-09-14 Xiang Tang, Hsian-Hua Tseng
We formulate and study an extension of gerbe duality to relative Gromov–Witten theory.
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Probing the Big Bang with quantum fields Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-07-11 Abhay Ashtekar, Tommaso De Lorenzo, Marc Schneider
By carrying out a systematic investigation of linear, test quantum fields $\hat{\varphi}(x)$ in cosmological space-times, we show that $\hat{\varphi}(x)$ remain well-defined across the big bang as operator valued distributions in a large class of Friedmann, Lemaître, Robertson, Walker space-times, including radiation and dust filled universes. In particular, the expectation values $\hat{\varphi}(x)
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Module constructions for certain subgroups of the largest Mathieu group Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-07-11 Lea Beneish
For certain subgroups of $M_{24}$, we give vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of Mathieu moonshine. The construction is related to the Conway moonshine module and employs a technique introduced by Anagiannis–Cheng–Harrison. With this construction
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A positive mass theorem for static causal fermion systems Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-07-11 Felix Finster, Andreas Platzer
Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat spacetime and a vacuum spacetime near spatial infinity. Our definition does not involve any regularity assumptions; it even applies to singular or generalized “quantum” spacetimes. A positive mass theorem is
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Adjoint Reidemeister torsions from wrapped M5-branes Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-07-11 Dongmin Gang, Seonhwa Kim, Seokbeom Yoon
We introduce a vanishing property of the adjoint Reidemeister torsion of a cusped hyperbolic $3$-manifold derived from the physics of wrapped M5-branes on the manifold. To support our physical observation, we present a rigorous proof for the figure-eight knot complement with respect to all slopes. We also present numerical verification for several knots.
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Two-dimensional perturbative scalar QFT and Atiyah–Segal gluing Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-07-11 Santosh Kandel, Pavel Mnev, Konstantin Wernli
We study the perturbative quantization of $2$-dimensional massive scalar field theory with polynomial (or power series) potential on manifolds with boundary. We prove that it fits into the functorial quantum field theory framework of Atiyah–Segal. In particular, we prove that the perturbative partition function defined in terms of integrals over configuration spaces of points on the surface satisfies
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Symplectic duality and implosions Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-24 Andrew Dancer, Amihay Hanany, Frances Kirwan
We discuss symplectic and hyperkähler implosion and present candidates for the symplectic duals of the universal hyperkähler implosion for various groups.
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Twisted gauge fields Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-24 Jordan François
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than representations of the structure group. We devise a notion of connection generalising Ehresmann connection on principal bundles, giving rise to the appropriate covariant derivative on sections of these twisted associated bundles (and on twisted tensorial forms). We
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Advening to adynkrafields: Young tableaux to component fields of the 10D, $\mathcal{N}=1$ scalar superfield Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-24 S. James Gates, Yangrui Hu, S.-N. Hazel Mak
Starting from higher dimensional adinkras constructed with nodes referenced by Dynkin Labels, we define “adynkras.” These suggest a computationally direct way to describe the component fields contained within supermultiplets in all superspaces. We explicitly discuss the cases of ten dimensional superspaces. We show this is possible by replacing conventional $\theta$-expansions by expansions over Young
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A proposal for nonabelian $(0,2)$ mirrors Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-24 Wei Gu, Jirui Guo, Eric Sharpe
In this paper we give a proposal for mirrors to $(0,2)$ supersymmetric gauged linear sigma models (GLSMs), for those $(0,2)$ GLSMs which are deformations of $(2,2)$ GLSMs. Specifically, we propose a construction of $(0,2)$ mirrors for $(0,2)$ GLSMs with $E$ terms that are linear and diagonal, reducing to both the Hori–Vafa prescription as well as a recent $(2,2)$ nonabelian mirrors proposal on the
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The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-24 Jonatan Lenells, Julien Roussillon
We study the recently introduced family of confluent Virasoro fusion kernels $\mathcal{C}_k (b, \theta, \sigma_s, \nu)$. We study their eigenfunction properties and show that they can be viewed as non-polynomial generalizations of both the continuous dual $q$-Hahn and the big $q$-Jacobi polynomials. More precisely, we prove that: (i) $\mathcal{C}_k$ is a joint eigenfunction of four different difference
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Transgression of D-branes Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-17 Severin Bunk, Konrad Waldorf
Closed strings can be seen either as one-dimensional objects in a target space or as points in the free loop space. Correspondingly, a B‑field can be seen either as a connection on a gerbe over the target space, or as a connection on a line bundle over the loop space. Transgression establishes an equivalence between these two perspectives. Open strings require D‑branes: submanifolds equipped with vector
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Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-17 Herbert Clemens, Stuart Raby
Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $\mathbb{Z}_2$-action on the $F$-theory model in such a way that the $\mathbb{Z}_2$-quotient is Calabi–Yau with an Enriques GUT surface over which $SU(5)_{\operatorname{gauge}}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a
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$T$-duality, Jacobi forms and Witten–Gerbe modules Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-17 Fei Han, Varghese Mathai
In this paper, we extend the T-duality Hori maps in [3], inducing isomorphisms of twisted cohomologies on T-dual circle bundles, to graded Hori maps and show that they induce isomorphisms of twovariable series of twisted cohomologies on the T-dual circle bundles, preserving Jacobi form properties. The composition of the graded Hori map with its dual is equal to the Euler operator. We also construct
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Unbroken $E7 \times E7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals Adv. Theor. Math. Phys. (IF 1.5) Pub Date : 2022-06-17 Yusuke Kimura
Eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_8 \mathfrak{e}_7$ were constructed by Malmendier and Morrison as heterotic duals of F-theory on K3 surfaces with $\Lambda^{1,1} \otimes E_8 \otimes E_7$ lattice polarization. Clingher, Malmendier and Shaska extended these constructions to eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_7