Supersymmetric D3-branes in Five-Form Flux

TL;DR

This paper studies the effects of a self-dual five-form flux on multiple Euclidean D3-branes, proposing a deformed supersymmetric ${ m N}=4$ SYM action that incorporates the flux's influence.

Contribution

It introduces a novel deformation of ${ m N}=4$ SYM to include five-form flux effects and demonstrates how to supersymmetrize this modified action.

Findings

Derived the Chern-Simons term induced by the RR flux

Constructed a supersymmetric deformation of ${ m N}=4$ SYM

Identified supersymmetries preserved by the flux background

Abstract

We consider multiple Euclidean D3-branes in a specific supergravity solution, which consists of a self-dual 5-form RR field in a flat background. We propose a deformation of ${\cal N}=4$ SYM action describing the dynamics of D3-branes in this background. We look at the supersymmetries of ${\cal N}=4$ SYM theory consistent with those preserved by the background. We derive the Chern-Simons action induced by the RR field, and show that the whole action can be supersymmetrized. This we do by deforming the supersymmetry transformations and using the BRST-like characteristic of the unbroken supercharges.