Small instanton transitions for M5 fractions

TL;DR

This paper investigates the recombination and freezing phenomena of M5-branes at ADE singularities using anomaly matching, providing new insights into their Higgs moduli spaces and extending conjectures for related compactified theories.

Contribution

It introduces a novel anomaly-based method to compute Higgs moduli space dimensions for M5-branes on ADE singularities and extends existing conjectures to new compactification scenarios.

Findings

M5 fractions can recombine in multiple ways leaving frozen singularities

Anomaly polynomial constrains the nature of the freezing process

Extended conjectures for class S and affine-Dynkin quiver theories in lower dimensions

Abstract

M5-branes on an ADE singularity are described by certain six-dimensional "conformal matter" superconformal field theories. Their Higgs moduli spaces contain information about various dynamical processes for the M5s; however, they are not directly accessible due to the lack of a Lagrangian formulation. Using anomaly matching, we compute their dimensions. The result implies that M5 fractions can recombine in several different ways, where the M5s are leaving behind frozen versions of the singularity. The anomaly polynomial gives hints about the nature of the freezing. We also check the Higgs dimension formula by comparing it with various existing conjectures for the CFTs one obtains by torus compactifications down to four and three dimensions. Aided by our results, we also extend those conjectures to compactifications of theories not previously considered. These involve class S theories with twisted punctures in four dimensions, and affine-Dynkin-shaped quivers in three dimensions.