Supersymmetry of the D3/D5 Defect Field Theory

TL;DR

This paper analyzes the supersymmetry structure of the D3/D5 defect field theory, providing explicit variations, supercurrents, and algebra, and introduces new Bogomolny equations for supersymmetric configurations.

Contribution

It presents the full R-symmetry-covariant supersymmetry variations, supercurrents, and supercharge algebra for the D3/D5 system, and introduces a new form of Bogomolny equations for supersymmetric solutions.

Findings

Derived full supersymmetry variations and supercurrents.

Computed the supercharge algebra and central charges.

Identified new Bogomolny equations for supersymmetric configurations.

Abstract

Four-dimensional N=4 super Yang-Mills, with a codimension-one defect breaking half of the supersymmetry, arises as the field theory description of the D3/D5 intersection in the holographic limit. This is one of the earliest, most extensively studied, and commonly used systems in holography. In this note we give the full R-symmetry-covariant supersymmetry variations for this system. We also provide the supercurrents and compute the algebra of the corresponding supercharges, obtaining the full set of central charges. We show that magnetically charged finite-energy field configurations preserving half of the supersymmetry are solutions to a new form of the extended Bogomolny equations, in which the defect fields play the role of jumping data for the Nahm-like part of the equations. In the appendices, we explain the connection between our results and the superspace-based formulations in the literature.