Magnetic quivers and negatively charged branes

TL;DR

This paper explores the Higgs branches of theories involving multiple M5 branes on ALE spaces, revealing new geometric structures and physical phenomena through the use of magnetic quivers, especially in cases with negative brane numbers.

Contribution

It introduces a novel analysis of Higgs branches with boundary conditions involving negative branes using magnetic quivers, uncovering previously neglected models and geometric realizations.

Findings

Identification of new Higgs branch models with interesting physics

Analysis of negative brane numbers in D-type boundary conditions

Connection to nilpotent orbits, Slodowy slices, and symmetric products

Abstract

The Higgs branches of the world-volume theories for multiple M5 branes on an $A_k$ or $D_k$-type ALE space are known to host a variety of fascinating properties, such as the small $E_8$ instanton transition or the discrete gauging phenomena. This setup can be further enriched by the inclusion of boundary conditions, which take the form of $SU(k)$ or $SO(2k)$ partitions, respectively. Unlike the $A$-type case, $D$-type boundary conditions are eventually accompanied by negative brane numbers in the Type IIA brane realisation. While this may seem discouraging at first, we demonstrate that these setups are well-suited to analyse the Higgs branches via magnetic quivers. Along the way, we encounter multiple models with previously neglected Higgs branches that exhibit exciting physics and novel geometric realisations. Nilpotent orbits, Slodowy slices, and symmetric products.