Extended global symmetries for 4d N=1 SQCD theories

TL;DR

This paper explores how coupling 4d N=1 SQCD theories with 3 flavors to 5d hypermultiplets enhances their global symmetry from SU(6) to E_6, revealing extended symmetries and connections between indices across dimensions.

Contribution

It demonstrates the explicit enhancement of global symmetry from SU(6) to E_6 in reduced SQCD theories coupled to 5d hypermultiplets, extending previous duality and symmetry results.

Findings

SU(6) symmetry is enhanced to E_6 with 3 flavors

Connections established between 3d and 4d indices

Extended global symmetries in coupled 4d-5d theories

Abstract

In arXiv:0811.1909 Spiridonov and Vartanov, using the superconformal index technique, found that 4-dimensional N=1 SQCD theory with SU(2) gauge group and four flavors has 72 dual representations. Recently in arXiv:1209.1404 the authors showed that these dual theories, when coupled to 5d hypermultiplets with specific boundary conditions have an extended E_7 global symmetry. In this work we find that for a reduced theory with 3 flavors the explicit SU(6) global symmetry is enhanced to an E_6 symmetry in the presence of 5d hypermultiplets. We also show connections between indices of different theories in 3 and 4 dimensions.