A freely generated ring for N=1 models in class S_k

TL;DR

This paper investigates 4d N=1 class S_k theories derived from M5 branes on singularities, proposing a freely generated ring structure in their protected spectrum and deriving a related index limit.

Contribution

It introduces a conjecture that the protected spectrum of class S_k theories contains a freely generated ring, extending the Coulomb branch concept from N=2 theories, and provides a formula for the index limit.

Findings

Proposes a freely generated ring in the spectrum of class S_k theories.

Derives a limit of the supersymmetric index generalizing the Coulomb limit.

Provides a conjectured simple formula for the index in this limit.

Abstract

We study 4d N=1 supersymmetric theories of class S_k, obtained from flux compactifications on a Riemann surface of 6d (1,0) conformal theories describing the low energy physics on a stack of M5 branes probing a Z_k singularity. We conjecture that the protected spectrum of class S_k theories contains a freely generated ring, generalizing the Coulomb branch of the N=2 theories. We derive this by examining a limit of the supersymmetric index of 4d N=1 class S_k theories. The limit generalizes the Coulomb limit of N=2 theories, which coincides with the case of k=1 for a particular choice of flux. We conjecture a general simple formula for the index in the aforementioned limit.