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Unifying lattice models, links and quantum geometric Langlands via branes in string theory Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210908
Meer Ashwinkumar, MengChwan TanWe explain how, starting with a stack of D4branes ending on an NS5brane in type IIA string theory, one can, via Tduality and the topologicalholomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello’s 4d Chern–Simons theory, (ii) links in 3d analyticallycontinued Chern–Simons theory, (iii) the quantum geometric Langlands correspondence realized

Anomaly cancellation in the topological string Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210908
Kevin Costello, Si LiWe describe the coupling of holomorphic Chern–Simons theory at large $N$ with Kodaira–Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for openclosed topological $B$‑model. At one loop this anomaly cancellation is analogous to the Green–Schwarz mechanism. As an application, we introduce a type I version of Kodaira–Spencer theory in complex dimensions

Invertible phases of matter with spatial symmetry Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210908
Daniel S. Freed, Michael J. HopkinsWe propose a general formula for the group of invertible topological phases on a space $Y$, possibly equipped with the action of a group $G$. Our formula applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a crystallographic group, the term ‘topological crystalline phases’ is sometimes used for these phases of matter.

Opers, surface defects, and YangYang functional Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210908
Saebyeok Jeong, Nikita NekrasovWe explore the nonperturbative Dyson–Schwinger equations obeyed by the partition functions of the $\Omega$deformed $\mathcal{N}=2, d=4$ supersymmetric linear quiver gauge theories in the presence of surface defects. We demonstrate that the partition functions of different types of defects (orbifold or vortex strings) are related by analytic continuation. We introduce Darboux coordinates on a patch

Recounting special Lagrangian cycles in twistor families of K3 surfaces (or: How I learned to stop worrying and count BPS states) Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210908
Shamit Kachru, Arnav Tripathy, Max ZimetWe consider asymptotics of certain BPS state counts in Mtheory compactified on a K3 surface. Our investigation is parallel to (and was inspired by) recent work in the mathematics literature by Filip [1], who studied the asymptotic count of special Lagrangian fibrations of a marked K3 surface, with fibers of volume at most $V_\ast$, in a generic twistor family of K3 surfaces. We provide an alternate

On the conformal method for the Einstein constraint equations Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210707
Michael T. AndersonIn this work, we use the global analysis and degreetheoretic methods introduced by Smale to study the existence and multiplicity of solutions of the vacuum Einstein constraint equations given by the conformal method of Lichnerowicz–Choquet–Bruhat–York. In particular this approach gives a new proof of the existence result of Maxwell and Holst–Nagy–Tsogtgerel. We also relate the method to the limit

Degenerate quantum general linear groups Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210707
Jin Cheng, Yan Wang, Ruibin ZhangGiven any pair of positive integers m and n, we construct a new Hopf algebra, which may be regarded as a degenerate version of the quantum group of $\mathfrak{gl}_{m+n}$. We study its structure and develop a highest weight representation theory. The finite dimensional simple modules are classified in terms of highest weights, which are essentially characterised by $m + n  2$ nonnegative integers and

Evaluating quasilocal angular momentum and centerofmass at null infinity Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210707
Jordan Keller, YeKai Wang, ShingTung YauWe calculate the limits of the quasilocal angular momentum and centerofmass defined by Chen–Wang–Yau [11] for a family of spacelike twospheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi–Sachs expansion. Our result complements earlier work of Chen–Wang–Yau [12], where the authors calculate the limits of the quasilocal energy and linear momentum at null

JT gravity and the ensembles of random matrix theory Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20210707
Douglas Stanford, Edward WittenWe generalize the recently discovered relationship between JT gravity and doublescaled random matrix theory to the case that the boundary theory may have timereversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Timereversal symmetry in the boundary theory means that unorientable

6D SCFTs and the classification of homomorphisms $\Gamma_{ADE} \to E_8$ Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200601
Darrin D. Frey, Tom RudeliusWe elucidate the correspondence between a particular class of superconformal field theories in six dimensions and homomorphisms from discrete subgroups of $SU(2)$ into $E_8$, as predicted from string dualities. We show how this match works for homomorphisms from the binary icosahedral group $SL(2, 5)$ into $E_8$, correcting previous errors in both the mathematics and physics literature. We use this

Sampling with positive definite kernels and an associated dichotomy Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Palle Jorgensen, James TianWe study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels $K$ with the property that there are countable discrete samplesubsets $S$; i.e., proper subsets $S$ having the property that every function in $\mathscr{H}\left(K\right)$

Branes and categorifying integrable lattice models Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Meer Ashwinkumar, MengChwan Tan, Qin ZhaoWe elucidate how integrable lattice models described by Costello's 4d ChernSimons theory can be realized via a stack of D4branes ending on an NS5brane in type IIA string theory, with D0branes on the D4brane worldvolume sourcing a meromorphic RR 1form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d ChernSimons theory, and by applying

Geometric quantization via SYZ transforms Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Kwokwai Chan, YatHin SuenThe socalled quantization problem in geometric quantization is asking whether the space of wave functions is independent of the choice of polarization. In this paper, we apply SYZ transforms to solve the quantization problem in two cases: (1) semiflat Lagrangian torus fibrations over complete compact integral affine manifolds, and (2) projective toric manifolds. More precisely, we prove that the

Cubic hypergeometric integrals of motion in affine Gaudin models Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Sylvain Lacroix, Benoît Vicedo, Charles YoungWe construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with the quadratic Hamiltonians. We prove that their vacuum eigenvalues, and their eigenvalues for one Bethe root, are given by certain hypergeometric functions

On Hochschild invariants of Landau–Ginzburg orbifolds Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Dmytro ShklyarovWe develop an approach to calculating the cup and cap products on Hochschild cohomology and homology of curved algebras associated with polynomials and their finite abelian symmetry groups. For polynomials with isolated critical points, the approach yields a complete description of the products. We also reformulate the result for the corresponding categories of equivariant matrix factorizations. In

Twodimensional supersymmetric gauge theories with exceptional gauge groups Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Zhuo Chen, Wei Gu, Hadi Parsian, Eric SharpeWe apply the recent proposal for mirrors of nonabelian (2,2) supersymmetric twodimensional gauge theories to make predictions for twodimensional supersymmetric gauge theories with exceptional gauge groups G2, F4, E6, E7, and E8. We compute the mirror LandauGinzburg models and predict excluded Coulomb loci and Coulomb branch relations (quantum cohomology). We also discuss the relationship between

On the counting of $O(N)$ tensor invariants Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Remi C. Avohou, Joseph Ben Geloun, Nicolas Dub$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorithms computing their number at an arbitrary rank and

Small sphere limit of the quasilocal energy with anti deSitter space reference Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
PoNing ChenIn [13], a new quasilocal energy is introduced for spacetimes with a nonzero cosmological constant. In this article, we study the small sphere limit of this newly defined quasilocal energy for spacetimes with a negative cosmological constant. For such spacetimes, the anti deSitter space is used as the reference for the quasilocal energy. Given a point $p$ in a spacetime $N$, we consider a canonical

Symplectic coarsegrained dynamics: Chalkboard motion in classical and quantum mechanics Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Maurice A. de GossonIn the usual approaches to mechanics (classical or quantum) the primary object of interest is the Hamiltonian, from which one tries to deduce the solutions of the equations of motion (Hamilton or Schrodinger). In the present work we reverse this paradigm and view the motions themselves as being the primary objects. This is made possible by studying arbitrary phase space motions, not of points, but

Coupled gravitational and electromagnetic perturbations of Reissner–Nordström spacetime in a polarized setting Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Elena GiorgiWe derive a system of equations governing the coupled gravitational and electromagnetic perturbations of ReissnerNordstrom spacetime. The equations are derived in the context of global nonlinear stability of ReissnerNordstrom under axially symmetric polarized perturbations, as a generalization of the recent work on nonlinear stability of Schwarzschild spacetime of KlainermanSzeftel. The main result

Nilmanifolds and their associated nonlocal fields Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Juan J. VillarrealFor six dimensional nilmanifolds we build a module $\mathcal{H}$ of an affine Kac Moody vertex algebras. Then, we associate some logarithmic fields for the module $\mathcal{H}$ and we study their singularities. We also presented a physics motivation behind this construction. We study a particular case, we show that when the nilmanifold $N$ is a $k$ degree $S^1$fibration over the two torus and a choice

Projections, modules and connections for the noncommutative cylinder Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Joakim Arnlind, Giovanni LandiWe initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one can develop several concepts in a close analogy with the latter. In particular, we exhibit a countable number of nontrivial projections in the algebra of the noncommutative

Perturbation theory for critical points of causal variational principles Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Felix FinsterThe perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the pushforward under a dif feomorphism. Then the constructions are extended to convex combinations of such measures, leading to perturbation expansions for the mean and the fluctuation

Higher Tduality of super Mbranes Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Domenico Fiorenza, Hisham Sati, Urs SchreiberWe establish a higher generalization of super Linfinityalgebraic Tduality of super WZWterms for super pbranes. In particular, we demonstrate spherical Tduality of super M5branes propagating on exceptionalgeometric 11d super spacetime.

Homotopy algebras in higher spin theory Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Si Li, Keyou ZengMotivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation in terms of the MaurerCartan equation associated to differential forms valued in Linfinity algebras. The elimination of auxiliary variables of Vasiliev equation

Branched holomorphic Cartan geometry on Sasakian manifolds Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Indranil Biswas, Sorin Dumitrescu, Georg SchumacherWe extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian CalabiYau manifolds are investigated.

Chern–Simons theory on a general Seifert $3$manifold Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Matthias Blau, Kaniba Mady Keita, K. S. Narain, George ThompsonThe path integral for the partition function of ChernSimons gauge theory with a compact gauge group is evaluated on a general Seifert 3manifold. This extends previous results and relies on abelianisation, a background field method and local application of the Kawasaki Index theorem.

A variational principle for Kaluza–Klein types theories Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Frédéric HéleinFor any positive integer n and any Lie group G, given a definite symmetric bilinear form on R n and an Adinvariant scalar product on the Lie algebra of G, we construct a variational problem on fields defined on an arbitrary (n + dimG)dimensional manifold Y. We show that, if G is compact and simply connected, any global solution of the EulerLagrange equations leads to identify Y with the total space

A 3d gauge theory/quantum Ktheory correspondence Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Hans Jockers, Peter MayrThe 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kahler manifold X, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence, where the UV model is the N=2 supersymmetric 3d gauge theory and the IR limit is given by Givental's permutation equivariant quantum Ktheory on X. This gives a oneparameter deformation of the 2d GLSM/quantum

$SU(n) \times \mathbb{Z}_2$ in Ftheory on K3 surfaces without section as double covers of Halphen surfaces Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
Yusuke KimuraWe investigate Ftheory models with a discrete $\mathbb{Z}_2$ gauge symmetry and $SU(n)$ gauge symmetries. We utilize a class of rational elliptic surfaces lacking a global section, known as Halphen surfaces of index 2, to yield genusone fibered K3 surfaces with a bisection, but lacking a global section. We consider Ftheory compactifications on these K3 surfaces times a K3 surface to build such models

On entropy for general quantum systems Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20200101
W. A. Majewski, L. E. LabuschagneIn these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied within the recently developed Orlicz space based approach to large systems. This means that the proposed approach successfully provides a refined framework for the

Representations of the loop braid group and Aharonov–Bohm like effects in discrete $(3+1)$dimensional higher gauge theory Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Alex Bullivant, João Faria Martins, Paul MartinWe show that representations of the loop braid group arise from AharonovBohm like effects in finite 2group (3+1)dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call Wbikoids (welded bikoids). Our main example of Wbikoids arises from finite 2groups, realised as crossed modules of groups. Given a Wbikoid, and hence a groupoid of

Asymptotically flat extensions with charge Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Aghil Alaee, Armando J. Cabrera Pacheco, Carla CederbaumThe Bartnik mass is a notion of quasilocal mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is wellcontrolled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this

Rigidity of asymptotically $AdS_2 \times S^2$ spacetimes Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Gregory J. Galloway, Melanie GrafThe spacetime $AdS_2 \times S^2$ is well known to arise as the 'near horizon' geometry of the extremal ReissnerNordstrom solution, and for that reason it has been studied in connection with the AdS/CFT correspondence. Here we consider asymptotically $AdS_2 \times S^2$ spacetimes that obey the null energy condition (or a certain averaged version thereof). In support of a conjecture of Juan Maldacena

Knotsquivers correspondence Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Piotr Kucharski, Markus Reineke, Marko Stošić, Piotr SułkowskiWe introduce and explore the relation between knot invariants and quiver representation theory, which follows from the identification of quiver quantum mechanics in Dbrane systems representing knots. We identify various structural properties of quivers associated to knots, and identify such quivers explicitly in many examples, including some infinite families of knots, all knots up to 6 crossings

Local and global existence of solutions to scalar equations on spatially flat universe as a background with nonminimal coupling Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Fiki T. Akbar, Bobby E. Gunara, Muhammad Iqbal, Hadi SusantoWe prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$order linear energy and the corresponding energy norm. In the local case, we show that both the $k$order linear energy and the energy norm are bounded for finite time with initial data in $H^{k+1}\times H^{k}$. Whereas in

Variation and rigidity of quasilocal mass Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Siyuan Lu, Pengzi MiaoInspired by the work of ChenZhang \cite{ChenZhang}, we derive an evolution formula for the WangYau quasilocal energy in reference to a static space, introduced by ChenWangWangYau \cite{CWWY}. If the reference static space represents a mass minimizing, static extension of the initial surface $\Sigma$, we observe that the derivative of the WangYau quasilocal energy is equal to the derivative

Symmetry classification of topological photonic crystals Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Giuseppe De Nittis, Max LeinIn a seminal paper Haldane conjectured that topological phenomena are not particular to quantum systems, and indeed experiments realized unidirectional, backscatteringfree edge modes with electromagnetic waves. This raises two immediate questions: (1) Are there other topological effects in electromagnetic media? And (2) is Haldane's Quantum Hall Effect for light really analogous to the Quantum Hall

$\mathrm{S}$ duality and framed BPS states via BPS graphs Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Dongmin Gang, Pietro Longhi, Masahito YamazakiWe study a realization of S dualities of fourdimensional $\mathcal{N}=2$ class $\mathcal{S}$ theories based on BPS graphs. S duality transformations of the UV curve are explicitly expressed as a sequence of topological transitions of the graph, and translated into cluster transformations of the algebra associated to the dual BPS quiver. Our construction applies to generic class $\mathcal{S}$ theories

A local and operational framework for the foundations of physics Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Robert OecklWe discuss a novel framework for physical theories that is based on the principles of locality and operationalism. It generalizes and unifies previous frameworks, including the standard formulation of quantum theory, the convex operational framework and Segal's approach to quantum field theory. It is capable of encoding both classical and quantum (field) theories, implements spacetime locality in a

Homotopy classes of gauge fields and the lattice Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Claudio Meneses, José A. ZapataFor a smooth manifold $M$, possibly with boundary and corners, and a Lie group $G$, we consider a suitable description of gauge fields in terms of parallel transport, as groupoid homomorphisms from a certain path groupoid in $M$ to $G$. Using a cotriangulation $\mathscr{C}$ of $M$, and collections of finitedimensional families of paths relative to $\mathscr{C}$, we define a homotopical equivalence

On the positivity of trace class operators Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Elena Cordero, Maurice de Gosson, Fabio NicolaThe characterization of positivity properties of Weyl operators is a notoriously difficult problem, and not much progress has been made since the pioneering work of Kastler, Loupias, and MiracleSole (KLM). In this paper we begin by reviewing and giving simpler proofs of some known results for traceclass Weyl operators; the latter play an essential role in quantum mechanics. We then apply timefrequency

Electrovacuum spacetime near an extreme horizon Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Carmen Li, James LuciettiWe determine all infinitesimal transverse deformations of extreme horizons in EinsteinMaxwell theory that preserve axisymmetry. In particular, we show that the general static transverse deformation of the AdS(2) X S(2) nearhorizon geometry is a twoparameter family, which contains the known extreme charged, accelerating, static black hole solution held in equilibrium by an external electric or magnetic

A Laplace transform approach to linear equations with infinitely many derivatives and zetanonlocal field equations Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
A. Chávez, H. Prado, E. G. ReyesWe study existence, uniqueness and regularity of solutions for linear equations in infinitely many derivatives. We develop a natural framework based on Laplace transform as a correspondence between appropriate $L^p$ and Hardy spaces: this point of view allows us to interpret rigorously operators of the form $f(\partial_t)$ where $f$ is an analytic function such as (the analytic continuation of) the

Covariance of the classical Brink–Schwarz superparticle Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Ezra Getzler, Sean Weinz PohorenceWe show that the classical BrinkSchwarz superparticle is a generalized AKSZ field theory. We work in the BatalinVilkovisky formalism: the main technical tool is the vanishing of BatalinVilkovisky cohomology below degree 1.

The twodimensional Coulomb plasma: quasifree approximation and central limit theorem Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Roland Bauerschmidt, Paul Bourgade, Miika Nikula, HorngTzer YauFor the twodimensional onecomponent Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1\kappa}$ for some constant $\kappa > 0$. This expansion is based on approximating the Coulomb gas by a quasifree Yukawa gas. Further, we prove that the fluctuations of the linear statistics are given by a

Topological surgery in cosmic phenomena Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Stathis Antoniou, Louis H. Kauffman, Sofia LambropoulouWe connect topological changes that can occur in $3$space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole formation. By considering the initial manifold as the $3$dimensional spatial section of spacetime, we describe the changes of topology occurring in these processes

Real bundle gerbes, orientifolds and twisted $KR$homology Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Pedram Hekmati, Michael K. Murray, Richard J. Szabo, Raymond F. VozzoWe consider Real bundle gerbes on manifolds equipped with an involution and prove that they are classified by their Real DixmierDouady class in Grothendieck's equivariant sheaf cohomology. We show that the Grothendieck group of Real bundle gerbe modules is isomorphic to twisted KRtheory for a torsion Real DixmierDouady class. Using these modules as building blocks, we introduce geometric cycles

Calabi–Yau manifolds realizing symplectically rigid monodromy tuples Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Charles F. Doran, Andreas MalmendierWe define an iterative construction that produces a family of elliptically fibered CalabiYau $n$folds with section from a family of elliptic CalabiYau varieties of one dimension lower. Parallel to the geometric construction, we iteratively obtain for each family with a point of maximal unipotent monodromy, normalized to be at t=0, its PicardFuchs operator and a closedform expression for the period

Topological phases on the hyperbolic plane: fractional bulkboundary correspondence Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Varghese Mathai, Guo Chuan ThiangWe study topological phases in the hyperbolic plane using noncommutative geometry and Tduality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models used in the Euclidean setting, a model for the bulkboundary correspondence of fractional indices is proposed, guided by the geometry of hyperbolic boundaries.

Moduli and periods of supersymmetric curves Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Giulio Codogni, Filippo VivianiSupersymmetric curves are the analogue of Riemann surfaces in super geometry. We establish some foundational results about complex DeligneMumford superstacks, and we then prove that the moduli superstack of supersymmetric curves is a smooth complex DeligneMumford superstack. We then show that the superstack of supersymmetric curves admits a coarse complex superspace, which, in this case, is just

BVBFV approach to General Relativity: Palatini–Cartan–Holst action Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
A. S. Cattaneo, M. SchiavinaWe show that the PalatiniCartanHolst formulation of General Relativity in tetrad variables must be complemented with additional requirements on the fields when boundaries are taken into account for the associated BV theory to induce a compatible BFV theory on the boundary.

Complete solution of a gauged tensor model Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Chethan Krishnan, K. V. Pavan KumarBuilding on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for all the singlet eigenstates and eigenvalues of the simplest nonlinear ($n=2, d=3$) gauged GurauWitten tensor model. This solves the theory completely. The ground state eigenvalue is $2\sqrt{14}$ in suitable conventions. This matches the result obtained for the ground state energy in the ungauged model

Graph minors and the linear reducibility of Feynman diagrams Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Benjamin Moore, Karen YeatsWe look at a graph property called reducibility which is closely related to a condition developed by Brown to evaluate Feynman integrals. We show for graphs with a fixed number of external momenta, that reducibility with respect to both Symanzik polynomials is graph minor closed. We also survey the known forbidden minors and the known structural results. This gives some structural information on those

On nondegeneracy of Riemannian Schwarzschildanti de Sitter metrics Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Piotr T. Chruściel, Erwann Delay, Paul KlingerWe prove that the $TT$gaugefixed linearised Einstein operator is nondegenerate for Riemannian Kottler ("Schwarzschildanti de Sitter") metrics with dimension and topologydependent ranges of mass parameter. We provide evidence that this remains true for all such metrics except the spherical ones with a critical mass.

Some applications of the mirror theorem for toric stacks Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Tom Coates, Alessio Corti, Hiroshi Iritani, HsianHua TsengWe use the mirror theorem for toric DeligneMumford stacks, proved recently by the authors and by CheongCiocanFontanineKim, to compute genuszero GromovWitten invariants of a number of toric orbifolds and gerbes. We prove a mirror theorem for a class of complete intersections in toric DeligneMumford stacks, and use this to compute genuszero GromovWitten invariants of an orbifold hypersurface

Bialgebras, the classical Yang–Baxter equation and Manin triples for 3Lie algebras Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Chengming Bai, Li Guo, Yunhe ShengThis paper studies two types of 3Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycles and double constructions respectively, and are therefore called the local cocycle 3Lie bialgebra and the double construction 3Lie bialgebra. They can be regarded as suitable extensions of the wellknown Lie bialgebra in the context of 3Lie algebras

Entropy formula and conserved charges of $\textrm{Spin3}$ ChernSimonslike theories of gravity Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
M. R. Setare, H. AdamiIn this paper we present the generalization of ChernSimonslike theories of gravity (CSLTG) to spin3. We propose a Lagrangian describing the spin3 fields coupled to ChernSimonslike theories of gravity. Then we obtain conserved charges of these theories by using a quasilocal formalism. We find a general formula for entropy of black holes solutions of Spin3 CSLTG. As an example, we apply our formalism

Ring objects in the equivariant derived Satake category arising from Coulomb branches Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Alexander Braverman, Michael Finkelberg, Hiraku NakajimaThis is the second companion paper of arXiv:1601.03586. We consider the morphism from the variety of triples introduced in arXiv:1601.03586 to the affine Grassmannian. The direct image of the dualizing complex is a ring object in the equivariant derived category on the affine Grassmannian (equivariant derived Satake category). We show that various constructions in arXiv:1601.03586 work for an arbitrary

Embeddings of complex supermanifolds Adv. Theor. Math. Phys. (IF 1.276) Pub Date : 20190101
Kowshik BettadapuraIn this article we present a study of embeddings of complex supermanifolds. We are broadly guided by the question: when will a submanifold of a split supermanifold itself be split? As an application of our study, we will address this question for certain superspace embeddings over rational normal curves.