Related papers: A Modular Invariant Partition Function for the Fiv…

Inspired by 5d supersymmetric Yang-Mills theories placed on the compact space $\mathbb{S}^5$, we propose an intriguing algebraic construction for the $q$-Virasoro algebra. We show that, when multiple $q$-Virasoro "chiral" sectors have to be…

We show that there exist infinitely many pairs of non-homeomorphic closed oriented SOL torus bundles with the same quantum (TQFT) invariants. This follows from the arithmetic behind the conjugacy problem in $SL(2,\Z)$ and its congruence…

We construct the full effective action including DBI and WZ terms for solitonic 5-branes covariant under T-duality. The result is a completion of results known in the literature to a full T-duality covariant expression. The covariant WZ…

We propose a way of computing 4-manifold invariants, old and new, as chiral correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of…

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular…

We derive some consistency conditions for fivebrane in M theory on R^5/Z_2 orbifold from the quantization law for the antisymmetric tensor field. We construct consistent fivebrane configurations in R^5/Z_2 type orbifold that exhibit the…

We consider an analogue of Witten's $SL(2,\mathbb{Z})$ action on three-dimensional QFTs with $U(1)$ symmetry for $2k$-dimensional QFTs with $\mathbb{Z}_2$ $(k-1)$-form symmetry. We show that the $SL(2,\mathbb{Z})$ action only closes up to a…

We study the (2,0) superconformal theories in six dimensions, which arise from the low-energy limit of k coincident 5-branes, using their discrete light-cone formulation as a superconformal quantum mechanical sigma model. We analyze the…

We introduce and study a Schwarz space S in the space of functions on the real line. It is a module over the algebra L of regular functions on the (modular double of the) non-commutative q-deformation of the moduli space of configurations…

We explore the $\mathbb{Z}_{2,3,4,6}$ S-foldings of some 5d superconformal field theories from the $(p,q)$ 5-brane web perspective. The S-folding involves both a spatial quotient and an $\mathrm{SL}(2,\mathbb{Z})$ transformation on 5-branes…

The partition function of a massless scalar field on a Euclidean spacetime manifold $\mathbb{R}^{d-1}\times\mathbb{T}^2$ and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is…

Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the…

Five-branes lead in four dimensions to massless N=1 supermultiplets if M-theory is compactified on S1/Z2 x (a Calabi-Yau threefold). One of them describes the modulus associated with the position of the five-brane along the circle S1. We…

We consider M-theory in the presence of M parallel M5-branes probing a transverse A_{N-1} singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of…

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become…

It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of…

In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components and the spin group is…

We show how the SL(5) duality in M-theory is explained from a canonical analysis of M2-brane mechanics. Diffeomorphism constraints for a M2-brane coupled to supergravity background in d=4 are reformulated in a SL(5) covariant form, in which…

A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations…