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

TL;DR

The paper develops a 4D BF-type topological action to describe the confining phase of $SU(N)$ Yang-Mills and its supersymmetric extension, encoding Aharonov-Bohm phases of center charges and flux-tube intersections. It shows that domain walls acquire a worldvolume Chern-Simons term at level $N$ and that electric flux tubes can end on walls, with a dynamical theta-angle implemented via a $B\wedge B$ term and a multi-branch structure labeled by $k$. In the SUSY case, the gluino-condensate phase acts as an axion that is eaten by a 3-form, giving a massive 3-form and screening that preserves BPS constraints, while in non-SUSY YM a long-range electric effect persists. The work connects to string-theory brane pictures and fractional quantum Hall physics, offering a cohesive topological framework for nonlocal operator dynamics and providing a foundation for exploring domain-wall dynamics across different contexts.

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.

Figures (4)

• Figure 1: $\theta$-dependence of the energy for the $N$ branches
• Figure 2: Flux tube connecting two probe charges
• Figure 3: Flux tube ending on the domain wall
• Figure 4: Vacua in Super-Yang-Mills theories