Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM

TL;DR

This paper explores the low-energy dynamics of 4D N=1 SYM domain walls via a 3D supersymmetric gauge theory, using string theory brane configurations to reveal dualities and new insights into brane behavior.

Contribution

It provides a geometric reformulation of domain wall properties and proposes a Seiberg-like duality for the Acharya-Vafa theory using string and field theory techniques.

Findings

Reformulation of N=1 SYM domain wall properties in geometric language

Proposal of a Seiberg-like duality for the Acharya-Vafa theory

New insights into brane dynamics preserving two supersymmetries

Abstract

We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint matter preserving two supersymmetries. According to Acharya and Vafa, this theory describes the low-energy worldvolume dynamics of BPS domain walls in four-dimensional N=1 SYM theory. We demonstrate how to obtain the same theory in a brane configuration of type IIB string theory that contains threebranes and fivebranes. A combination of string and field theory techniques allows us to re-formulate some of the well-known properties of N=1 SYM domain walls in a geometric language and to postulate a Seiberg-like duality for the Acharya-Vafa theory. In the process, we obtain new information about the dynamics of branes in setups that preserve two supersymmetries. Using similar methods we also study other N=1 CS theories with extra matter in the adjoint and fundamental representations of the gauge group.