Solitons in Supersymmetric Gauge Theories

TL;DR

This paper reviews recent advances in understanding BPS solitons in supersymmetric gauge theories, including their moduli spaces, composite states, and dynamics, with exact solutions in certain limits and examples illustrating complex soliton interactions.

Contribution

It provides a comprehensive review of BPS solitons in SUSY gauge theories, including new solutions, moduli space descriptions, and phenomena like wall transmutation and soliton interactions.

Findings

Moduli space of walls is a complex Grassmann manifold.

All 1/4 BPS composite soliton solutions are obtained in the strong coupling limit.

Walls can coexist with monopoles and vortices, exhibiting complex interactions.

Abstract

Recent results on BPS solitons in the Higgs phase of supersymmetric (SUSY) gauge theories with eight supercharges are reviewed. For U(N_C) gauge theories with the N_F(>N_C) hypermultiplets in the fundamental representation, the total moduli space of walls are found to be the complex Grassmann manifold SU(N_F)/[SU(N_C)xSU(N_F-N_C)xU(1)]. The monopole in the Higgs phase has to accompany vortices, and preserves a 1/4 of SUSY. We find that walls are also allowed to coexist with them. We obtain all the solutions of such 1/4 BPS composite solitons in the strong coupling limit. Instantons in the Higgs phase is also obtained as 1/4 BPS states. As another instructive example, we take U(1)xU(1) gauge theories with four hypermultiplets. We find that the moduli space is the union of several special Lagrangian submanifolds of the Higgs branch vacua of the corresponding massless theory. We also observe transmutation of walls and repulsion and attraction of BPS walls. This is a review of recent works on the subject, which was given at the conference by N.Sakai.