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The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we provide a classification for regular distributions on rational normal scrolls and weighted projective spaces. Additionally, under specific conditions, we prove that the singular set of a codimension one holomorphic foliation on a compact toric orbifold admits at least one irreducible component of codimension two, and we also present a Darboux–Jouanolou type integrability theorem for codimension one holomorphic foliations. Our results are exemplified through various illustrative examples. [ABSTRACT FROM AUTHOR]

We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer–Manin obstruction interpolating between Manin's classical version for rational points and the integral version developed by Colliot-Thélène and Xu. We determine the status of local-global principles, and obstructions to them, in two families of orbifolds naturally associated to quadric hypersurfaces. Further, we establish a quantitative result measuring the failure of the semi-integral Brauer–Manin obstruction to account for its integral counterpart for affine quadrics. [ABSTRACT FROM AUTHOR]

The non-hyperelliptic connected components of the strata of translation surfaces are conjectured to be orbifold classifying spaces for some groups commensurable to some mapping class groups. The topological monodromy map of the non-hyperelliptic components projects naturally to the mapping class group of the underlying punctured surface and is an obvious candidate to test commensurability. In the present article, we prove that for the components |$\mathcal {H}(3,1)$| and |$\mathcal {H}^{nh}(4)$| in genus 3 the monodromy map fails to demonstrate the conjectured commensurability. In particular, building on the work of Wajnryb, we prove that the kernels of the monodromy maps for |$\mathcal {H}(3,1)$| and |$\mathcal {H}^{nh}(4)$| are large, as they contain a non-abelian free group of rank |$2$|⁠. [ABSTRACT FROM AUTHOR]

In this work we study families of ℤ2 orbifolds of toroidal conformal field theories based on both factorizable and non-factorizable target space tori. For these classes of theories, we analyze their moduli spaces, and compute their partition functions. Building on previous work, we express the calculated partition functions in terms of suitable Siegel-Narain theta functions that allow us to determine their ensemble averages. We express the derived averaged partition functions of the studied families of conformal field theories in a manifest modular invariant finite sum of products of real analytic Eisenstein series. We speculate on a tentative holographic three-dimensional dual bulk interpretations for the considered ℤ2 orbifold classes of ensembles of conformal field theories. [ABSTRACT FROM AUTHOR]

This paper is about the orbifold theory of affine vertex operator superalgebras. Among the main results, we classify the irreducible modules and determine the fusion rules for the orbifold of the simple affine vertex operator superalgebra L o s p (1 | 2) ˆ (k , 0). [ABSTRACT FROM AUTHOR]

We explore connections among Monstrous Moonshine, orbifolds, the Kitaev chain and topological modular forms. Symmetric orbifolds of the Monster CFT, together with further orbifolds by subgroups of Monster, are studied and found to satisfy the divisibility property, which was recently used to rule out extremal holomorphic conformal field theories. For orbifolds by cyclic subgroups of Monster, we arrive at divisibility properties involving the full McKay–Thompson series. Orbifolds by non-abelian subgroups of Monster are further considered by utilizing the data of Generalized Moonshine. [ABSTRACT FROM AUTHOR]

We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where we excite one copy of the seed CFT with a left-moving superconformal descendant. When the theory is deformed away from this region of moduli space these states can 'lift', despite being BPS at the orbifold point. For descendants formed from the supersymmetry and R-symmetry current modes we obtain explicit results for the expectation value of the lifts for various subfamilies of states at second order in the deformation parameter. A smooth ∼ behaviour is observed in the lifts of these subfamilies for large dimensions. Using covering space Ward identities we then find a compact expression for the lift of the above descendant states valid for arbitrary dimensions. In the large-dimension limit this lift scales as ∼ , strengthening the conjecture that this is a universal property of the lift of D1-D5-P states. We observe that the lift is not simply a function of the total dimension, but depends on how the descendant level is partitioned amongst modes. [ABSTRACT FROM AUTHOR]

In this work we study interesting corners of the quantum gravity landscape with 8 supercharges pushing the boundaries of our current understanding. Calabi-Yau threefolds compactifications of F/M/type II theories to 6, 5 and 4 dimensions are the most prominent examples of this class, and these always lead to a universal hypermultiplet coming from the volume/string coupling constant. We find new examples of asymmetric orbifold constructions which have no hypermultiplets in 4 or 5 dimensions and no neutral hypers in 6d. We argue that these theories can also be obtained by going to strong coupling/small volume regions of geometric constructions where a new Coulomb branch opens up and moving in this direction freezes the volume/string coupling constant. Interestingly we find that the Kodaira condition encountered in geometric limits of F-theory compactifications to 6 dimensions is violated in these corners of the landscape due to strong quantum corrections. We also construct a theory in 3 dimensions which if it were to arise by toroidal compactifications from 5d, it would have to come from pure N = 1 supergravity with no massless scalar fields. [ABSTRACT FROM AUTHOR]

Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds M /ℤ, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results. [ABSTRACT FROM AUTHOR]

The bound state of one NS5 brane (wrapped on a 핋4) and N NS1-branes has two dual descriptions: its low-energy dynamics is described by the symmetric orbifold of 핋4, while the near horizon geometry is captured by string theory on AdS3 × S3 × 핋4 with one unit of NS flux. The latter theory is exactly solvable in the hybrid formalism, and this allows one to prove the equivalence of the two descriptions. In this paper we extend this duality to ℤk orbifolds of this AdS3 × S3 background. In particular, we show that the corresponding worldsheet spectrum reproduces exactly the perturbative excitations on top of a certain non-perturbative state in the dual symmetric orbifold theory. Since the AdS/CFT duality map is exact for these models, we obtain an interesting picture of how the duality relates boundary and bulk descriptions. [ABSTRACT FROM AUTHOR]

We compute the structure constants of topological symmetric orbifold theories up to third order in the large N expansion. The leading order structure constants are dominated by topological metric contractions. The first order interactions are single cycles joining while at second order we can have double joining as well as splitting. At third order, single cycle joining obtains genus one contributions. We also compute illustrative small N structure constants. Our analysis applies to all second quantized Frobenius algebras, a large class of algebras that includes the cohomology ring of the Hilbert scheme of points on K3 among many others. We point out interesting open questions that our results raise. [ABSTRACT FROM AUTHOR]

In this work, we study the realization of non-invertible duality symmetries along the toroidal branch of the c = 2 conformal manifold. A systematic procedure to construct symmetry defects is implemented to show that all Rational Conformal Field Theories along this branch enjoy duality symmetries. Furthermore, we delve into an in-depth analysis of two representative cases of multicritical theories, where the toroidal branch meets various orbifold branches. For these particular examples, the categorical data and the defect Hilbert spaces associated with the duality symmetries are obtained by resorting to modular covariance. Finally, we study the interplay between these novel symmetries and the various exactly marginal and relevant deformations, including some representative examples of Renormalization Group flows where the infrared is constrained by the non-invertible symmetries and their anomalies. [ABSTRACT FROM AUTHOR]

We study the correlations of pairs of complex logarithms of Z -lattice points in C at various scalings, proving the existence of pair correlation functions. We prove that at the linear scaling, the pair correlations exhibit level repulsion, as it sometimes occurs in statistical physics. We prove total loss of mass phenomena at superlinear scalings, and Poissonian behaviour at sublinear scalings. The case of Euler weights has applications to the pair correlation of the lengths of common perpendicular geodesic arcs from the maximal Margulis cusp neighbourhood to itself in the Bianchi orbifold PSL 2 (Z [ i ]) \ H R 3 . [ABSTRACT FROM AUTHOR]

We define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe -structures on this ring and a power structure over it. We show that the conjectual symmetric power of the projective line with several orbifold points described by A. Fonarev is consistent with the symmetric power of this line with the set of distinguished points as a pair of varieties. [ABSTRACT FROM AUTHOR]

We study several aspects of fillings for links of general isolated quotient singularities using Floer theory, including co‐fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on the non‐existence of exact fillings of contact links of isolated terminal quotient singularities. We provide an extensive list of isolated terminal quotient singularities whose contact links are not exactly fillable, including Cn/(Z/2)${\mathbb {C}}^n/({\mathbb {Z}}/2)$ for n⩾3$n\geqslant 3$, which settles a conjecture of Eliashberg, quotient singularities from general cyclic group actions and finite subgroups of SU(2)$SU(2)$, and all terminal quotient singularities in complex dimension 3. We also obtain uniqueness of the orbifold diffeomorphism type of exact orbifold fillings of contact links of some isolated terminal quotient singularities. [ABSTRACT FROM AUTHOR]

Exercise is essential for mastering mathematics, but it faces two major hurdles. First, students are often not motivated to do their homework. Second, checking traditional homework is a manual and labor-intensive process that becomes harder to support as the number of students increases. We argue that computer games could alleviate both problems. In contrast to homework, students are willing to spend many hours playing video games. And because video games keep track of the gamers' performance, they offer a scalable solution to the problem of checking the homework. We describe an experiment to augment traditional homework with a computer game that we have developed for exercising the topics of symmetry groups in an undergraduate college course. We describe the mathematical background of the subject matter, how we have embedded the mathematics into the game, the empirical results of playing the game, and the insights we have gained from this experiment. [ABSTRACT FROM AUTHOR]

Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized symmetries in two-dimensional QFT. Such symmetries are described by topological defect lines (TDLs) which obey fusion rules that are non-invertible in general. Despite this seemingly exotic feature, all well-known properties in gauging invertible symmetries carry over to this general setting, which greatly enhances both the scope and the power of gauging. This is established by formulating generalized gauging in terms of topological interfaces between QFTs, which explains the physical picture for the mathematical concept of algebra objects and associated module categories over fusion categories that encapsulate the algebraic properties of generalized symmetries and their gaugings. This perspective also provides simple physical derivations of well-known mathematical theorems in category theory from basic axiomatic properties of QFT in the presence of such interfaces. We discuss a bootstrap-type analysis to classify such topological interfaces and thus the possible generalized gaugings and demonstrate the procedure in concrete examples of fusion categories. Moreover we present a number of examples to illustrate generalized gauging and its properties in concrete conformal field theories (CFTs). In particular, we identify the generalized orbifold groupoid that captures the structure of fusion between topological interfaces (equivalently sequential gaugings) as well as a plethora of new self-dualities in CFTs under generalized gaugings. [ABSTRACT FROM AUTHOR]

We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space. [ABSTRACT FROM AUTHOR]

In the D1D5 CFT the twist operator of order 2 can twist together two copies in the untwisted sector into a single joined copy in the twisted sector. Traditionally, this effect is computed by using the covering map method. Recently, a new method was developed using the Bogoliubov ansatz and conformal symmetry to compute this effect in a toy model of one free boson. In this paper, we use this method with superconformal symmetry to compute the effect of the twist operator in the D1D5 CFT. This may provide more effective tools for computing correlation functions of twist operators in this system. [ABSTRACT FROM AUTHOR]

We discuss the theory of equivariant localization focussing on applications relevant for holography. We consider geometries comprising compact and non-compact toric orbifolds, as well as more general non-compact toric Calabi–Yau singularities. A key object in our constructions is the equivariant volume, for which we describe two methods of evaluation: the Berline–Vergne fixed point formula and the Molien–Weyl formula, supplemented by the Jeffrey–Kirwan prescription. We present two applications in supersymmetric field theories. Firstly, we describe a method for integrating the anomaly polynomial of SCFTs on compact toric orbifolds. Secondly, we discuss equivariant orbifold indices that are expected to play a key role in the computation of supersymmetric partition functions. In the context of supergravity, we propose that the equivariant volume can be used to characterize universally the geometry of a large class of supersymmetric solutions. As an illustration, we employ equivariant localization to prove the factorization in gravitational blocks of various supergravity free energies, recovering previous results as well as obtaining generalizations. [ABSTRACT FROM AUTHOR]

We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an n - 1 -dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension 2 n + 1 which are n - 1 -connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3 orbifold, there exist four seven-dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki–Einstein. [ABSTRACT FROM AUTHOR]

The work presented considers a class of minimally constructed Yukawa unified SUSY GUTs - NUHM2 - and explores their implications when their soft supersymmetry breaking Lagrangian is generalized by the nonholomorphic terms which provide extra contributions to the Higgsino mass and couple the supersymmetric scalar fields to the wrong Higgs doublets. With such a simple extension, it can be found several regions with interesting implications which cannot be realized in the usual restricted models. It is observed that the Yukawa unification solutions can be compatible with a relatively light mass spectrum and acceptable low fine-tuning measurements. In the restricted models such effects can directly be addressed to the nonholomorphic terms. They can provide a slight improvement in the SM-like Higgs boson mass without altering the mass spectrum too much, and they can accommodate relatively lighter sbottom and stau masses, while they do not change the stop sector much. The dark matter can be Higgsino-like or Bino-like, but the experimental relic density measurements favor the Higgsino-like dark matter, while the Bino-like dark matter is predicted with a quite large relic density. Also, several coannihilation scenarios are identified in the Higgsino-like dark matter regions, while the Bino-like dark matter does not allow any of such coannihilation processes. The presence of the nonholomorphic terms can weaken the impact from the phenomenological or indirect constraints such as low fine-tuning, Yukawa unification, and rare decays of B-meson, the direct and model-independent constraints still yield a strong strike on the solutions. Such constraints are discussed regarding the current collider analyses on τ τ events and direct detection of dark matter experiments. [ABSTRACT FROM AUTHOR]

We define a notion of Heegaard Floer homology for three-dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected. [ABSTRACT FROM AUTHOR]

We construct the quantum curve for the Baker–Akhiezer function of the orbifold Gromov–Witten theory of the weighted projective line ℙ[r]. Furthermore, we deduce the explicit bilinear Fermionic formula for the (stationary) Gromov–Witten potential via the lifting operator contructed from the Baker–Akhiezer function. [ABSTRACT FROM AUTHOR]

We describe a method for deriving surface functionalization patterns for colloidal systems that can induce self-assembly into any chosen periodic symmetry at a planar interface. The result is a sequence of letters, s ∈ {A,T,C,G}, or a gene, that describes the perimeter of the colloidal object and programs its self-assembly. This represents a genome that is finite and can be exhaustively enumerated. These genes derive from symmetry, which may be topologically represented by two-dimensional parabolic orbifolds; since these orbifolds are surfaces that may be derived from first principles, this represents an ab initio route to colloid functionality. The genes are human readable and can be employed to easily design colloidal units. We employ a biological (genetic) analogy to demonstrate this and illustrate their connection to the designs of Maurits Cornelis (M. C.) Escher. [ABSTRACT FROM AUTHOR]

The moduli space of holomorphic differentials on curves of genus g admits a natural action of the group . The study of orbits of this action and their closures has attracted the interest of a wide range of researchers in the last few decades. In the 2000s, C. McMullen described an infinite family of orbifolds that are closures of such orbits in the space of holomorphic differentials on curves of genus 2. In spaces of holomorphic differentials on curves of higher genera, well-known examples of orbifolds that are unions of -orbit closures are Prym eigenform loci. They are nonempty for surfaces of genus at most 5. This paper presents the first nontrivial calculations of the number of connected components in Prym eigenform loci for surfaces of maximum possible genus. [ABSTRACT FROM AUTHOR]

We prove the existence of infinitely many alternating links in S 3 whose complements are commensurable with the Bianchi orbifold ℍ 3 / PSL (2 , O 1 5). [ABSTRACT FROM AUTHOR]

We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equipped with Hofer's metric, prove constraints on Lagrangian packing, find instances of Lagrangian Poincaré recurrence, and present a new hierarchy of normal subgroups of area-preserving homeomorphisms of the two-sphere. The technology involves Lagrangian spectral invariants with Hamiltonian term in symmetric product orbifolds. [ABSTRACT FROM AUTHOR]

We establish rigid tensor category structure on finitely-generated weight modules for the subregular W-algebras of sl n at levels - n + n n + 1 (the B n + 1 -algebras of Creutzig–Ridout–Wood) and at levels - n + n + 1 n (the finite cyclic orbifolds of the β γ -vertex algebra), as well as for their Feigin–Semikhatov dual principal W-superalgebras of sl n | 1 . These categories are neither finite nor semisimple, and in the W-algebra case they contain modules with infinite-dimensional conformal weight spaces and no lower bound on conformal weights. We give complete lists of indecomposable projective modules in these tensor categories and fusion rules for simple modules. All these vertex operator (super)algebras are simple current extensions of singlet algebras tensored with a rank-one Heisenberg algebra, so we more generally study simple current extensions in direct limit completions of vertex algebraic tensor categories. Then our results for W-(super)algebras follow from the known ribbon category structure on modules for the singlet algebras. Our results include and generalize those of Allen-Wood on the β γ -vertex algebra, as well as our own on the affine vertex superalgebra of gl 1 | 1 . Our results also include the first examples of ribbon category structure on all finitely-generated weight modules for an affine vertex algebra at a non-integral admissible level, namely for affine sl 2 at levels - 4 3 and - 1 2 . [ABSTRACT FROM AUTHOR]

Let G be a finite subgroup of \mathrm {SU}(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient {\mathbb {C}}^4/G, and conjecture a closed formula for their generating series in terms of the root system of G. In the second part, we define degree zero Donaldson-Thomas invariants of Calabi-Yau 4-orbifolds, develop a vertex formalism that computes the invariants in the toric case, and conjecture closed formulae for their generating series for the quotient stacks [{\mathbb {C}}^4/{\mathbb {Z}}_r], [{\mathbb {C}}^4/{\mathbb {Z}}_2\times {\mathbb {Z}}_2]. Combining these two parts, we formulate a crepant resolution correspondence which relates the above two theories. [ABSTRACT FROM AUTHOR]

The species scale provides an upper bound for the ultraviolet cutoff of effective theories of gravity coupled to a number of light particle species. Modular invariant (super‐)potentials provide a simple and computable expression of the species scale as a function of the moduli in toroidal orbifold compactifications of type II and heterotic string are pointed out. Due t o modular symmetry, these functions are valid over all moduli space and not only in asymptotic regions. Additive logarithmic corrections to the species scale arise from the requirement that the latter be modular invariant are observed. The moduli‐dependent expression of the species scale in terms of the gravitino mass or the scalar potential of these models are recasted and swampland conjectures such as the anti‐de Sitter distance conjecture and the gravitino conjecture are connected. The species scale provides an upper bound for the ultraviolet cutoff of effective theories of gravity coupled to a number of light particle species. Modular invariant (super‐)potentials provide a simple and computable expression of the species scale as a function of the moduli in toroidal orbifold compactifications of type II and heterotic string are pointed out. Due to modular symmetry, these functions are valid over all moduli space and not only in asymptotic regions. Additive logarithmic corrections to the species scale arise from the requirement that the latter be modular invariant are observed. The moduli‐dependent expression of the species scale in terms of the gravitino mass or the scalar potential of these models are recasted and swampland conjectures such as the anti‐de Sitter distance conjecture and the gravitino conjecture are connected. [ABSTRACT FROM AUTHOR]

In this work we study particular TQFTs in three dimensions, known as Symmetry Topological Field Theories (or SymTFTs), to identify line defects of two-dimensional CFTs arising from the compactification of 6d (2, 0) SCFTs on 4-manifolds M4. The mapping class group of M4 and the automorphism group of the SymTFT switch between different absolute 2d theories or global variants. Using the combined symmetries, we realize the topological defects in these global variants. Our main example is ℙ1 × ℙ1. For N M5-branes the corresponding 2d theory inherits ℤN 0-form symmetries from the SymTFT. We reproduce the orbifold groupoid for theories with ℤN 0-form symmetries and realize the duality defects at fixed points of the coupling constant under elements of the mapping class group. We also study other Hirzebruch surfaces, del Pezzo surfaces, as well as the connected sum of ℙ1 × ℙ1. We find a rich network of global variants connected via automorphisms and realize more interesting topological defects. Finally, we derive the SymTFT on more general 4-manifolds and provide two examples. [ABSTRACT FROM AUTHOR]

Massive type IIA flux compactifications of the form AdS4 × X6, where X6 admits a Calabi-Yau metric and O6-planes wrapping three-cycles, display families of vacua with parametric scale separation between the compactification scale and the AdS4 radius, generated by an overall rescaling of internal four-form fluxes. For toroidal orbifolds one can perform two T-dualities and map this background to an orientifold of massless type IIA compactified on an SU(3)-structure manifold with fluxes. Via a 4d EFT analysis, we generalise this last construction and embed it into new branches of supersymmetric and non-supersymmetric vacua with similar features. We apply our results to propose new infinite families of vacua based on elliptic fibrations with metric fluxes. Parametric scale separation is achieved by an asymmetric flux rescaling which, however, in general is not a simple symmetry of the 4d equations of motion. At this level of approximation the vacua are stable but, unlike in the Calabi-Yau case, they display a non-universal mass spectrum of light fields. [ABSTRACT FROM AUTHOR]

We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS 3 solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS 2 solutions of D = 11 supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS 3 solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell c-function in the dual field theory, establishing a very general exact result in holography. For the AdS 2 solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS 4 . [ABSTRACT FROM AUTHOR]

We use the exact degeneracy formula of single-centred 1 4 BPS dyonic black holes with unit torsion in 4D N = 4 toroidally compactified heterotic string theory to improve on the existing formulation of the corresponding quantum entropy function obtained using supersymmetric localization. The result takes the form of a sum over Euclidean backgrounds including orbifolds of the Euclidean AdS 2 × S 2 attractor geometry. Using an N = 2 formalism, we determine the explicit form of the Abelian gauge potentials supporting these backgrounds. We further show how a rewriting of the degeneracy formula is amenable, at a semi-classical level, to a gravitational interpretation involving 2D Euclidean wormholes. This alternative picture is useful to elucidate different aspects of the gravitational path integral capturing the microstate degeneracies. We also comment on the relation between the associated 1D holographic models. [ABSTRACT FROM AUTHOR]

We examine how conformal boundaries encode energy transport coefficients — namely transmission and reflection probabilities — of corresponding conformal interfaces in symmetric orbifold theories. These constitute a large class of irrational theories and are closely related to holographic setups. Our central goal is to compare such coefficients at the orbifold point (a field theory calculation) against their values when the orbifold is highly deformed (a gravity calculation) — an approach akin to past AdS/CFT-guided comparisons of physical quantities at strong versus weak coupling. At the orbifold point, we find that the (weighted-average) transport coefficients are simply averages of coefficients in the underlying seed theory. We then focus on the symmetric orbifold of the 핋4 sigma model interface CFT dual to type IIB supergravity on the 3d Janus solution. We compare the holographic transmission coefficient, which was found by [1], to that of the orbifold point. We find that the profile of the transmission coefficient substantially increases with the coupling, in contrast to boundary entropy. We also present some related ideas about twisted-sector data encoded by boundary states. [ABSTRACT FROM AUTHOR]

Conical defects of the form (AdS3 × S 3 )/ℤk have an exact orbifold description in worldsheet string theory, which we derive from their known presentation as gauged Wess-Zumino-Witten models. The configuration of strings and fivebranes sourcing this geometry is well-understood, as is the correspondence to states/operators in the dual CFT2. One can analytically continue the construction to Euclidean AdS3 (i.e. the hyperbolic ball ℍ 3 + ) and consider the orbifold by any infinite discrete (Kleinian) group generated by a set of elliptic elements γi ∈ SL(2, ℂ), γ i k i = ퟙ, i = 1,... , K. The resulting geometry consists of multiple conical defects traveling along geodesics in ℍ 3 + , and provides a semiclassical bulk description of correlation functions in the dual CFT involving the corresponding defect operators, which is nonperturbatively exact in α′. The Lorentzian continuation of these geometries describes a collection of defects colliding to make a BTZ black hole. We comment on a recent proposal to use such correlators to prepare a basis of black hole microstates, and elaborate on a picture of black hole formation and evaporation in terms of the underlying brane dynamics in the bulk. [ABSTRACT FROM AUTHOR]

On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected n-orbifolds are manifolds. The latter improves the best previously known bound of Lytchak by roughly a factor of 2. For compact orbifolds and in most dimensions, we prove slightly better bounds. We obtain sharp results up to dimension 5. [ABSTRACT FROM AUTHOR]

To a positive-definite even lattice Q, one can associate the lattice vertex algebra VQ, and any automorphism σ of Q lifts to an automorphism of VQ. In this paper, we investigate the orbifold vertex algebra VQσ, which consists of the elements of VQ fixed under σ, in the case when σ has prime order. We describe explicitly the irreducible VQσ-modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible VQσ-modules. We consider in detail the cases when the order of σ is 2 or 3, as well as the case of permutation orbifolds. [ABSTRACT FROM AUTHOR]

We give a graph-sum algorithm that expresses any genus-g Gromov-Witten invariant of the symmetric product orbifold \operatorname {Sym}^d\mathbb {P}^r≔ [(\mathbb {P}^r)^d/S_d] in terms of "Hurwitz-Hodge integrals" – integrals over (compactified) Hurwitz spaces. We apply the algorithm to prove a mirror-type theorem for \operatorname {Sym}^d\mathbb {P}^r in genus zero. The theorem states that a generating function of Gromov-Witten invariants of \operatorname {Sym}^d\mathbb {P}^r is equal to an explicit power series I_{\operatorname {Sym}^d\mathbb {P}^r}, conditional upon a conjectural combinatorial identity. This is a first step in the direction of proving Ruan's Crepant Resolution Conjecture for the resolution Hilb^{(d)}(\mathbb {P}^2) of the coarse moduli space of \operatorname {Sym}^d\mathbb {P}^2. [ABSTRACT FROM AUTHOR]

We investigate the limit of sequences of vertex algebras. We discuss under what condition the vector space direct limit of such a sequence is again a vertex algebra. We then apply this framework to permutation orbifolds of vertex operator algebras and their large N limit. We establish that for any nested oligomorphic permutation orbifold such a large N limit exists, and we give a necessary and sufficient condition for that limit to factorize. This helps clarify the question of what VOAs can give rise to holographic conformal field theories in physics. [ABSTRACT FROM AUTHOR]

We study 4-dimensional SU(N) × U(1) gauge theories with a single massless Dirac fermion in the 2-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible 0-form ℤ ~ 2 N ± 2 χ chiral symmetry along with a 1-form ℤ N 1 center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus T 3, we construct the non-unitary gauge invariant operator corresponding to ℤ ~ 2 N ± 2 χ and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject T 3 to ℤ N 1 twists, for N even, in selected magnetic flux sectors, the algebra of ℤ ~ 2 N ± 2 χ and ℤ N 1 fails to commute by a ℤ2 phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the 1-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary T 3 size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an appendix, we also discuss how to construct the corresponding noninvertible defect via the "half-space gauging" of a discrete one-form magnetic symmetry. [ABSTRACT FROM AUTHOR]

The cobordism conjecture implies that consistent theories of Quantum Gravity must admit the introduction of boundaries. We study the dynamical realization of the cobordism conjecture in type IIB in AdS5 × S5, using the existing gravity duals of 4d 풩 = 4 SYM with Gaiotto-Witten superconformal boundary conditions (near-horizon limits of D3-branes ending on NS5- and D5-branes). We show that these configurations are, from the 5d perspective, dynamical cobordism solutions which start from an asymptotic AdS5 vacuum and evolve until they hit an end of the world (ETW) brane with AdS4 worldvolume. The latter displays localization of gravity, and provide a completion of the Karch-Randall (KR) AdS branes, in which the backreaction of running scalars replace the KR cusp in the warp factor with a smooth bump. The dynamical scalars are either in the SO(6) invariant AdS5 bulk sector (e.g. describing the S5 size and its shrinking at the cobordism boundary) or brane localized (e.g. the SO(6) SO(3) × SO(3) squashing due to boundary conditions). We introduce a novel double scaling limit which zooms into the ETW brane and makes localization of gravity manifest, and which shows a tantalizing relation with wedge holography. We extend the picture to AdS5 theories with less (super)symmetry, via orbifolds and S-folds, leading to dynamical cobordisms for gravity duals of 4d theories with 풩 = 2 and 풩 = 3 supersymmetry. [ABSTRACT FROM AUTHOR]

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in physics, state a version of the decomposition conjecture, and then compute in numerous examples, checking that decomposition works as advertised. [ABSTRACT FROM AUTHOR]

We study four-dimensional superconformal field theories living on the worldvolume of D3 branes probing minimally-supersymmetric F-theory backgrounds, focusing on the case of orbi-orientifold setups with and without 7-branes. We observe that these theories are closely related to compactifications of six-dimensional 풩 = (1, 0) theories on a torus with flux, where the flux quanta is mapped in Type IIB to the defining data of the orbifold group. We analyze the cases of class 풮k theories as well as of compactifications of the E-string and of orbi-instanton theories. We also classify 풮-fold configurations in F-theory preserving minimal supersymmetry in four dimensions and their mass deformations. [ABSTRACT FROM AUTHOR]

We study freely acting orbifolds of type IIB string theory on T5 that spontaneously break supersymmetry from N = 8 to N = 6, 4, 2 or 0 in five dimensions. We focus on orbifolds that are a ℤp quotient by a T-duality acting on T4 and a shift on the remaining S1. Modular invariant partition functions are constructed and detailed examples of both symmetric and asymmetric orbifolds are presented, including new examples of five-dimensional non-supersymmetric string theories with no tachyons. The orbifolds we consider arise at special points in the moduli space of string theory compactifications with a duality twist. The supergravity limit of these are Scherk-Schwarz reductions which generate gauged supergravities with positive definite classical potentials on the moduli space in five dimensions. Both symmetric and asymmetric freely acting orbifolds give a landscape of Minkowski vacua. For gauged supergravities to belong to this landscape, we find a number of constraints and conditions. Firstly, the scalar potential should lead to a massive spectrum with masses that obey quantization conditions arising from a string theory orbifold, which we discuss in detail. Secondly, we find constraints on the massless sector, e.g. in the examples of orbifolds preserving sixteen supersymmetries in five dimensions that we consider, only an odd number of vector multiplets arises. Lastly, we present new examples of candidate asymmetric orbifolds with modular invariant partition functions, but with non-integral coefficients in the q q ¯ -expansion in the twisted sectors. [ABSTRACT FROM AUTHOR]

We compute all worldsheet three-point functions involving spectrally-flowed operators in chiral multiplets of the space-time theory for strings in AdS3×S3×T4, thus completing the analysis of the full AdS3/CFT2 chiral ring. We make use of techniques recently developed for the bosonic sector, based on holomorphic covering maps from the worldsheet to the AdS3 boundary. We highlight the role of the so-called series identifications when dealing with the complications originated by picture-changing spectrally-flowed states. We find an exact agreement with the predictions from the holographic CFT at the symmetric orbifold point. [ABSTRACT FROM AUTHOR]

We analyze the chiral operator ring of the symmetric orbifold conformal field theory on the complex two-plane ℂ2. We compute the large N limit of the ring and exhibit its factorized leading order behaviour. We moreover calculate all structure constants at the subleading and sub-subleading order. These features are coded as properties of the symmetric group and we review the relevant mathematical theorems on the product of conjugacy classes in the center of the group algebra. We illustrate the efficiency of the formalism by iteratively computing broad classes of higher point extremal correlators. We point out generalizations of our simplest of models and argue that our combinatorial analysis is relevant to the organization of the large N perturbation theory of generic symmetric orbifolds. [ABSTRACT FROM AUTHOR]

We obtain non-trivial approximate solutions to the heterotic \mathrm {G}_2 system on the total spaces of non-trivial circle bundles over Calabi–Yau 3-orbifolds, which satisfy the equations up to an arbitrarily small error, by adjusting the size of the S^1 fibres in proportion to a power of the string constant \alpha '. Each approximate solution provides a cocalibrated \mathrm {G}_2-structure, the torsion of which realises a non-trivial scalar field, a constant (trivial) dilaton field and an H-flux with non-trivial Chern–Simons defect. The approximate solutions also include a connection on the tangent bundle which, together with a non-flat \mathrm {G}_2-instanton induced from the horizontal Calabi–Yau metric, satisfy the anomaly-free condition, also known as the heterotic Bianchi identity. The approximate solutions fail to be genuine solutions solely because the connections on the tangent bundle are only \mathrm {G}_2-instantons up to higher order corrections in \alpha '. [ABSTRACT FROM AUTHOR]

The universal two-parameter W ∞ -algebra is a classifying object for vertex algebras of type W (2 , 3 , ... , N) for some N. Gaiotto and Rapčák recently introduced a large family of such vertex algebras called Y -algebras, which includes many known examples such as the principal W -algebras of type A. These algebras admit an action of Z 2 , and in this paper we study the structure of their orbifolds. Aside from the extremal cases of either the Virasoro algebra or the W 3 -algebra, we show that these orbifolds are generated by a single field in conformal weight 4, and we give strong finite generating sets. [ABSTRACT FROM AUTHOR]