Related papers: Modified elliptic gamma functions and 6d superconf…
We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition…
We study the superconformal indices of 4d theories coming from 6d N=(2,0) theory of type \Gamma on a Riemann surface, with the action of the outer-automorphism \sigma in the trace. We find that the indices are given by the partition…
This is the second paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated in mathematical physics. In the first article in this series we defined geometric families of these functions…
Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
We suggest a supergravity dual for the $(1,0)$ superconformal field theory in six dimensions which has $E_8$ global symmetry. Compared to the description of the (2,0) field theory, the 4-sphere is replaced by a 4-hemisphere, or by…
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 uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field…
In this paper we describe a systematic method to compute elliptic genera of (2,2) supersymmetric gauge theories in two dimensions with gauge group G/Gamma (for G semisimple and simply-connected, Gamma a subgroup of the center of G) with…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
We derive the couplings of the 3-form supermultiplet to the general supergravity-matter-Yang-Mills system. Based on the methods of superspace geometry, we identify component fields, establish their supergravity transformations and construct…
We analyze higher-group structure of a 6d model coupled with a self-dual 2-form gauge field. This model is defined from 6d axion-electrodynamics with a 1-form Chern-Weil(CW) symmetry gauged dynamically. The gauging leads to a…
The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S^3 x S^1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect…
We construct novel $7d$ supersymmetric gauge theories which include a Chern-Simons-like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7-branes in type IIA$^*$ theory, rather than making use of an…
We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum…
We show the modular properties of the multiple 'elliptic' gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's…
In this paper we treat certain elliptic and hyper-elliptic integrals in a unified way. We introduce a new basis of these integrals coming from certain basis ${\phi}_n(x)$ of polynomials and show that the transition matrix between this basis…
We introduce the topologically twisted index for four-dimensional $\mathcal N=1$ gauge theories quantized on ${\rm AdS}_2 \times S^1$. We compute the index by applying supersymmetric localization to partition functions of vector and chiral…
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
We discuss possible observational manifestations of static, spherically symmetric solutions of a class of multidimensional theories of gravity, which includes the low energy limits of supergravities and superstring theories as special…