The Non-Abelian Self Dual String on the Light Cone

TL;DR

This paper constructs a scalar profile for a non-abelian self dual string connecting M5-branes on a light-like circle, using a modified Nahm's equations approach related to D2 and D4-branes with magnetic fields.

Contribution

It introduces a novel construction of the scalar profile for the non-abelian self dual string on light-like compactified M5-branes via a modified Nahm's equations framework.

Findings

Scalar profile remains finite in the infinite boost limit.

Solution exhibits smooth interpolation between phases.

Correct Higgs field value at infinity.

Abstract

We construct the scalar profile for the non-abelian self dual string connecting two M5-branes compactified on a light-like circle. The construction is based on a conjectured modified version of Nahm's equations describing a D2-brane, with a magnetic field on it, suspended between two D4-branes. Turning on a constant magnetic field on the D2-brane corresponds to a boost in the eleventh direction. In the limit of infinite boost the D4-branes correspond to light-like compactified M5-branes. The solution for the scalar profile of the brane remains finite in this limit and displays all the correct expected features such as smooth interpolation between the unbroken and broken phase with the correct value for the Higgs field at infinity.