Fibrations and Hasse diagrams for 6d SCFTs

TL;DR

This paper explores the moduli space of 6d SCFTs on M5 branes, revealing new geometric structures and isolated symplectic singularities through brane and quiver techniques.

Contribution

It introduces a detailed analysis of discrete gauging effects on the Higgs branch and identifies new transverse slices and symplectic singularities in 6d SCFTs.

Findings

Discovery of new transverse slices between phases of 6d SCFTs

Identification of some slices with known symplectic singularities

Conjecture of two new isolated symplectic singularities

Abstract

We study the full moduli space of vacua of 6d worldvolume SCFTs on M5 branes probing an $A$-type singularity, focusing on the geometric incarnation of the discrete gauging mechanism which acts as a discrete quotient on the Higgs branch fibered over the tensor branch. We combine insights from brane constructions and magnetic quiver techniques, in which discrete gauging is implemented through the concept of decoration introduced in [arXiv:2202.01218]. We discover and characterize new transverse slices between phases of 6d SCFTs, identifying some of them with a family of isolated symplectic singularities recently discovered in [arXiv:2112.15494], and conjecturing the existence of two new isolated symplectic singularities.