Supersymmetric D3/D5 for massive defects on curved space

TL;DR

This paper constructs a holographic dual for supersymmetric gauge theories with massive defects on curved spaces, solving BPS equations for D5-brane embeddings and validating results via localization.

Contribution

It develops a D3/D5 brane model for massive supersymmetric defects on curved backgrounds, solving BPS equations and matching holographic and field theory results.

Findings

Explicit solutions for D5-brane embeddings with supersymmetric deformations.

Agreement between holographic calculations and localization results.

Validation of the D3/D5 probe brane approach for massive defects.

Abstract

We construct the holographic dual for $\mathcal N=4$ SYM on $\rm S^4$ and $\rm AdS_4$ coupled to massive $\mathcal N=2$ supersymmetric quenched flavor fields on a codimension-1 defect, which is $\rm S^3$ and $\rm AdS_3$, respectively. The holographic description is in terms of a D3/probe D5 brane system. We set up and reduce the BPS equations for D5-brane embeddings with arbitrary supersymmetric deformations and partly solve them at the non-linear level. The remaining equations are solved explicitly in a small-mass expansion. We compute the contribution of the defect fields to the partition function on S$^4$ and compare to a field theory computation using supersymmetric localization, for which we set up the matrix model. Both computations agree, lending strong support to holographic probe brane constructions using D3/D5 configurations in general.