${\cal N}=1$ superfield description of BPS solutions in 6D gauged SUGRA with 3-branes

TL;DR

This paper develops an ${ m N}=1$ superfield framework for describing BPS solutions in six-dimensional gauged supergravity with 3-branes, simplifying background equations and aiding the derivation of 4D effective theories with preserved supersymmetry.

Contribution

It introduces a superfield approach to 6D supergravity with branes, simplifying the background equations and connecting to known component-field results.

Findings

Derived a simplified gauge for background equations.

Reproduced known results in component fields via Wess-Zumino gauge.

Identified a Liouville equation within the background equations.

Abstract

We provide ${\cal N}=1$ superfield description of BPS backgrounds in six-dimensional supergravity (6D SUGRA) with 3-branes, which is compactified on a two-dimensional space. The brane terms induce the localized fluxes. We find a useful gauge in which the background equations become significantly simple. This is not the Wess-Zumino gauge, and the relation to the usual component-field expression of 6D SUGRA is not straightforward. One of the equations reduces to the Liouville equation. By moving to the Wess-Zumino gauge, we check that our expressions reproduce the known results of the previous works, which are expressed in the component fields. Our results help us develop the systematic derivation of four-dimensional effective theories that keeps the ${\cal N}=1$ SUSY structure.