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

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.

26 pages, 5 figures

References in corpus (4)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• S-duality in N=2 supersymmetric gauge theories
• Four-Dimensional SCFTs from M5-Branes
• E-String Theory on Riemann Surfaces

Cited by in corpus (10)

• A slow review of the AGT correspondence
• From 6d flows to 4d flows
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Non minimal D-type conformal matter compactified on three punctured spheres
• Comments on Quivers and Fractons
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Hilbert Series of Bipartite Field Theories