Coulomb and Higgs Branches from Canonical Singularities: Part 0

TL;DR

This paper explores the geometric origins of 4d and 5d superconformal field theories from singularities, using resolutions, deformations, and mirror symmetry to analyze their Coulomb and Higgs branches, and computes their higher-form symmetries.

Contribution

It introduces a geometric framework connecting singularity resolutions to moduli spaces of SCFTs, including new insights into Higgs branches and higher-form symmetries.

Findings

Determined Higgs branches of some 5d SCFTs from geometry.

Linked singularities engineering Argyres-Douglas theories to rank-0 5d SCFTs.

Computed higher-form symmetries of 4d and 5d SCFTs.

Abstract

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $\mathcal{N}=4$ mirror symmetry and an $S$-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type $(G, G')$.