3d Mirror Symmetry from S-duality

TL;DR

This paper uses S-duality in type IIB string theory to relate partition functions of 5d supersymmetric theories and derives new 3d mirror pairs through Higgsing, revealing novel integral identities and defect structures.

Contribution

It introduces a method to obtain 3d mirror pairs from 5d theories via S-duality and Higgsing, leading to new hyperbolic integral identities and defect configurations.

Findings

Derived new 3d mirror pairs from 5d theories.

Established hyperbolic integral identities for partition functions.

Identified 3d defects on intersecting spaces.

Abstract

We consider type IIB $SL(2,\mathbb{Z})$ symmetry to relate the partition functions of different 5d supersymmetric Abelian linear quiver Yang-Mills theories in the $\Omega$-background and squashed $S^5$ background. By Higgsing S-dual theories, we extract new and old 3d mirror pairs. Generically, the Higgsing procedure yields 3d defects on intersecting spaces, and we derive new hyperbolic integral identities expressing the equivalence of the squashed $S^3$ partition functions with additional degrees of freedom on the $S^1$ intersection.