D-Branes in Field Theory

TL;DR

This work develops an open-string description for domain-wall D-branes in four-dimensional ${\cal N}=2$ SQCD, showing that wall dynamics are governed by a three-dimensional ${\cal N}=2$ Chern-Simons-Higgs theory on the wall worldvolume. For the abelian case, a pair of walls yields a chiral open-string multiplet whose integration generates a CS term with $\kappa=-\tfrac{1}{2}$ and a cigar-shaped moduli-space metric, reproducing the wall-ordering behavior seen in bulk moduli-space dynamics. The framework generalizes to multiple and non-Abelian walls, where the worldvolume theory becomes a product of ${U}(1)$ factors with bi-fundamental couplings and inter-wall CS terms, encoding the nontrivial wall-interaction structure and ordering. The paper also explores complex masses and FI parameters, deriving bound states and tachyonic instabilities, and discusses the connection to other D-brane systems and potential underlying string-theoretic pictures, highlighting open-closed duality in field theories without gravity.

Abstract

Certain gauge theories in four dimensions are known to admit semi-classical D-brane solitons. These are domain walls on which vortex flux tubes may end. The purpose of this paper is to develop an open-string description of these D-branes. The dynamics of the domain walls is shown to be governed by a Chern-Simons-Higgs theory which, at the quantum level, captures the classical "closed string" scattering of domain wall solitons.

Figures (2)

• Figure 1: The relative moduli space of two domain walls is a cigar.
• Figure 2: The ordering of many domain walls. The horizontal direction is their position, while the vertical denotes the type of domain wall.