Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
Oren Bergman, Amihay Hanany, Andreas Karch, Barak Kol
TL;DR
Bergman, Hanany, Karch, and Kol analyze three-dimensional gauge theories with Chern-Simons terms using Type II brane constructions of D3-branes between NS5 and $(p,q)$ 5-branes. They show that supersymmetry is dynamically broken when the number of D3-branes satisfies $n>|k|$, with the $N=3$ theory and certain $N=2$ and $N=1$ deformations breaking via the s-rule, while an instanton-generated repulsive potential breaks SUSY in the special $k=0$ $N=1$ case. The results are consistent with large-$|k|$ supersymmetric index calculations and provide a microscopic brane picture for the nonperturbative SUSY breaking, though subtleties remain for $|q|>1$ and non-integer CS levels. The work suggests further directions, including brane-box constructions to access purely $N=1$ YM-CS theories and a deeper understanding of infrared dynamics with fractional CS terms. Overall, the paper connects brane dynamics to dynamical SUSY breaking in 3D gauge theories with CS terms and clarifies the role of the s-rule and instanton effects in these systems.
Abstract
It is shown that supersymmetry is spontaneously broken in certain three-dimensional supersymmetric gauge theories, by using the s-rule in their string theory realization as brane configurations. In particular, supersymmetry is broken in N=3 supersymmetric Yang-Mills-Chern-Simons theory with gauge group SU(n) and CS coefficient k, as well as in its N=2 and N=1 deformations, when n>|k|. In addition, supersymmetry is broken in the N=1 mass deformation of N=2 supersymmetric Yang-Mills theory with gauge group SU(n) and one matter multiplet when n>1. In the latter case the breaking is induced by an instanton-generated repulsive potential.