Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model

TL;DR

This paper explores how the massive Yang-Mills-Chern-Simons matrix model can dynamically generate non-Abelian gauge groups, specifically demonstrating the emergence of nontrivial gauge groups as true vacua in certain parameter regions.

Contribution

It shows that the model's phase structure allows for the dynamical realization of nontrivial gauge groups, advancing understanding of gauge symmetry emergence in matrix models.

Findings

Existence of parameter regions with nontrivial gauge group vacua

Realization of O(N) copies of spin-1/2 representation as true vacuum

Analogies to transverse 5-branes in M-theory

Abstract

It has been known for some time that the dynamics of k coincident D-branes in string theory is described effectively by U(k) Yang-Mills theory at low energy. While these configurations appear as classical solutions in matrix models, it was not clear whether it is possible to realize the k =/= 1 case as the true vacuum. The massive Yang-Mills-Chern-Simons matrix model has classical solutions corresponding to all the representations of the SU(2) algebra, and provides an opportunity to address the above issue on a firm ground. We investigate the phase structure of the model, and find in particular that there exists a parameter region where O(N) copies of the spin-1/2 representation appear as the true vacuum, thus realizing a nontrivial gauge group dynamically. Such configurations are analogous to the ones that are interpreted in the BMN matrix model as coinciding transverse 5-branes in M-theory.