Related papers: On Higher Topological T-duality Functors

We introduce a notion of Poincar\'e duality for pairs of $\infty$-categories, extending Poincar\'e-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient book-keeping device that affords, among other things, a…

We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT's (Almost…

We prove a theorem classifying the equivariant $K$-theoretic pushforwards of the product of arbitrary Schur functors applied to the tautological bundle on the moduli space of framed rank $r$ torsion-free sheaves on $\mathbb{P}^2$, and its…

In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$…

We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for…

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

We define a "sutured topological quantum field theory", motivated by the study of sutured Floer homology of product 3-manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it…

We apply the $C^*$-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as…

We derive a component-field expansion of the Green-Schwarz action for the type IIA string, in an arbitrary background of massless NS-NS and R-R bosonic fields, up to quadratic order in the fermionic coordinates \theta. Using this action, we…

This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy types of their classifying spaces. Double categories (Ehresmann, 1963) have well-understood geometric realizations, and…

We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these…

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…

We develop a variant of calculus of functors, and use it to relate the gauge group G(P) of a principal bundle P over M to the Thom ring spectrum (P^Ad)^{-TM}. If P has contractible total space, the resulting Thom ring spectrum is LM^{-TM},…

The paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group $G$, a subgroup $K$), we construct categories, whose morphisms are two-dimensional surfaces tiled by polygons…

Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $\sigma$-models. They are constructed systematically…

We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the…

We point out that for N=4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with…

We analyze the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued fields, which is given by rectangular W-algebras with su$(M)$ symmetry. The matrix valued extension is expected to be useful for the relation between…

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT$_\pm [\mathcal{T}_{\rm rank \;0}]$, to a (2+1)D interacting $\mathcal{N}=4$ superconformal field theory (SCFT) $\mathcal{T}_{\rm…