Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions

TL;DR

This paper demonstrates that 't Hooft anomaly matching conditions in 4d supersymmetric theories can be derived from the modular properties of elliptic hypergeometric integrals, which describe superconformal indices.

Contribution

It establishes a novel connection between anomaly matching conditions and modular transformations of elliptic hypergeometric integrals.

Findings

't Hooft anomaly conditions follow from $SL(3, ext{Z})$-modular transformations

Superconformal indices are described by elliptic hypergeometric integrals

Modular properties encode duality relations in supersymmetric theories

Abstract

Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from $SL(3,\mathbb{Z})$-modular transformation properties of the kernels of dual indices.