Elliptic modular double and 4d partition functions

Abstract

We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic $W_{q,t;q^{\prime }}(\Gamma )$ algebras. We also consider a generating function of BPS surface defects supported on $T^2$ and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.

v1: 34 pages, 3 figures; v2: corrected few typos, references added

References in corpus (13)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Localization on Hopf surfaces
• Generalized Superconformal Index for Three Dimensional Field Theories
• Instantons on the 5-sphere and M5-branes
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Quivers, YBE and 3-manifolds
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Factorization of 4d N=1 superconformal index
• The modular properties and the integral representations of the multiple elliptic gamma functions
• Continuous biorthogonality of the elliptic hypergeometric function

Cited by in corpus (8)

• A slow review of the AGT correspondence
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Deconstructing Defects
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• Quasi-Hopf twist and elliptic Nekrasov factor
• Intersecting Surface defects and 3d Superconformal indices