M5-brane prongs, string soliton bound states and wall-crossing

TL;DR

This paper investigates BPS bound states of self-dual string solitons on M5-branes, revealing a molecule-like structure and wall-crossing behavior akin to string web configurations from D3-branes.

Contribution

It introduces a novel abelian M5-brane model capturing the equilibrium configurations of string solitons and elucidates wall-crossing phenomena in this context.

Findings

Molecule-like equilibrium of non-parallel string solitons

Deformation of M5-brane prongs into spikes and ridges

Wall-crossing behavior near marginal stability

Abstract

We study abelian M5-brane field configurations representing BPS bound states of self-dual string solitons whose locations correspond to the endlines of M2-branes ending on the M5-branes. The BPS equations are obtained from appropriate Bogomolny completion of the effective abelian low energy functional with two transverse scalars, using two vectors representing the directions along which these endline strings extend. Then we impose boundary conditions on the scalars near the string soliton cores. This leads to a molecule-like equilibrium structure of two non-parallel string solitons at fixed transverse separations, with the M5-brane "prong" deformations comprising two "spikes", each shaped like a ridge. The resulting picture becomes increasingly accurate as one approaches the wall of marginal stability, on which these states decay. There are various parallels with wall-crossing phenomena for string web configurations obtained from D3-brane deformations.