Isomorphisms of 4d N=2 SCFTs from 6d

TL;DR

This paper proves that certain 4d N=2 SCFTs constructed via different class S methods are actually equivalent by demonstrating the isomorphism of their underlying 6d SCFTs, using symmetry arguments and Higgs branch flows.

Contribution

It establishes the isomorphism of 6d SCFTs underlying different class S constructions of 4d N=2 theories, revealing their equivalence through symmetry analysis.

Findings

6d SCFTs are shown to be isomorphic.

Discrete symmetries relate different Higgs branch flows.

Different class S theories correspond to the same 6d SCFTs.

Abstract

There exist 4d $\mathcal{N}=2$ SCFTs in class $\mathcal{S}$ which have different constructions as punctured Riemann surfaces, but which nevertheless appear to describe the same physics. Some of these class $\mathcal{S}$ theories have an alternative construction as torus-compactifications of 6d $(1,0)$ SCFTs. We demonstrate that the 6d SCFTs are isomorphic. Each 6d SCFT in question can be obtained from a parent 6d SCFT by Higgs branch renormalization group flow, and the parent theory possesses a discrete symmetry under which the relevant Higgs branch flows are exchanged. The existence of this discrete symmetry, which may be embedded in an enhanced continuous symmetry, proves that the original pair of class $\mathcal{S}$ theories are, in fact, isomorphic.