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.

Highlights

  • One of the most beautiful features in the family of 3d gauge theories with N 1⁄4 4 supersymmetry is the existence of mirror symmetry [1]

  • One of our main results is a non-Abelian version of the basic SQED/ XYZ duality. This duality has implicitly appeared in [34] as an intermediate step to test the mirror dual of ðA1; A2n−1Þ Argyres-Douglas (AD) theories reduced to 3d, which has been shown to follow from an involved cascade of sequential confinement and mirror symmetry [20,21] starting from the 3d reduction of the 4d “Lagrangian” description [35,37]

  • This picture provides the generalization of the non-Abelian SQCDA/XYZ duality to the more complicated geometry involving 1d degrees of freedom, and we have shown that it descends from type IIB S-duality

Read more

Summary

INTRODUCTION

One of the most beautiful features in the family of 3d gauge theories with N 1⁄4 4 supersymmetry is the existence of mirror symmetry [1]. One of our main results is a non-Abelian version of the basic SQED/ XYZ duality This duality has implicitly appeared in [34] (at the level of the squashed S3 partition function) as an intermediate step to test the mirror dual of ðA1; A2n−1Þ Argyres-Douglas (AD) theories reduced to 3d, which has been shown to follow from an involved cascade of sequential confinement and mirror symmetry [20,21] starting from the 3d reduction of the 4d “Lagrangian” description [35,37]. A similar triality relation among distinct gauge theories has been recently obtained in 6d [66,67]

Duality frames
S5 partition functions
MIRROR SYMMETRY
Generalization
Quiver gauge theories
DISCUSSION AND OUTLOOK
The refined topological vertex
DIM intertwiners
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call