Star shaped quivers with flux

TL;DR

This paper investigates the compactification of 6d ${ m (2,0)}$ SCFTs on Riemann surfaces with flux, revealing dual descriptions of 3d class ${ m S}$ theories through reductions and mirror symmetry, supported by partition function tests.

Contribution

It introduces a new perspective on 3d class ${ m S}$ theories via reduction of 6d theories and generalizes star-shaped quiver dualities, including global property considerations.

Findings

Derived mirror dual descriptions of 3d theories

Generalized star-shaped quiver theories

Validated dualities through partition function calculations

Abstract

We study the compactification of the 6d ${\cal N}=(2,0)$ SCFT on the product of a Riemann surface with flux and a circle. On the one hand, this can be understood by first reducing on the Riemann surface, giving rise to 4d ${\cal N}=1$ and ${\cal N}=2$ class ${\cal S}$ theories, which we then reduce on $S^1$ to get 3d ${\cal N}=2$ and ${\cal N}=4$ class ${\cal S}$ theories. On the other hand, we may first compactify on $S^1$ to get the 5d ${\cal N}=2$ Yang-Mills theory. By studying its reduction on a Riemann surface, we obtain a mirror dual description of 3d class ${\cal S}$ theories, generalizing the star-shaped quiver theories of Benini, Tachikawa, and Xie. We comment on some global properties of the gauge group in these reductions, and test the dualities by computing various supersymmetric partition functions.