On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT

Abstract

We consider the 4d superconformal index for $\mathcal{N}=2$ gauge theories on $S^1\times L(r,1)$, where $L(r,1)$ is a Lens space. We focus on a one-parameter slice of the three-dimensional fugacity space and in that sector we show S-duality. We do so by rewriting the index in a way that resembles a correlation function of a 2d TFT, which however, we do not identify.

References in corpus (4)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• 5D SYM and 2D q-Deformed YM

Cited by in corpus (21)

• Down the rabbit hole with theories of class S
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Global Properties of Supersymmetric Theories and the Lens Space
• S-duality and the N=2 Lens Space Index
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• A slow review of the AGT correspondence
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• 4d $\mathcal{N}=3$ indices via discrete gauging
• Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra
• Equivariant Verlinde formula from fivebranes and vortices
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Lens space index and global properties for 4d N = 2 models
• Orbifold Schur Index and IR formula
• Aspects of 4d supersymmetric dynamics and geometry