Topological Model for Domain Walls in (Super-)Yang-Mills Theories

TL;DR

This paper develops a topological framework for understanding domain walls in (Super-)Yang-Mills theories, capturing key phases and linking to string theory and quantum Hall effects.

Contribution

It introduces a topological action that describes the confining phase and reveals the Chern-Simons term on domain walls, connecting field theory, string theory, and condensed matter analogies.

Findings

Topological action encodes all Aharonov-Bohm phases.

Domain walls contain a level N Chern-Simons term.

Connections to string theory and quantum Hall effect.

Abstract

We derive a topological action that describes the confining phase of (Super-)Yang-Mills theories with gauge group $SU(N)$, similar to the work recently carried out by Seiberg and collaborators. It encodes all the Aharonov-Bohm phases of the possible non-local operators and phases generated by the intersection of flux tubes. Within this topological framework we show that the worldvolume theory of domain walls contains a Chern-Simons term at level $N$ also seen in string theory constructions. The discussion can also illuminate dynamical differences of domain walls in the supersymmetric and non-supersymmetric framework. Two further analogies, to string theory and the fractional quantum Hall effect might lead to additional possibilities to investigate the dynamics.