Domain walls from ten dimensions

TL;DR

This paper derives conditions for supersymmetric four-dimensional domain walls from ten-dimensional supergravity using generalized complex geometry, connecting to effective theories and RG flows in the AdS/CFT framework.

Contribution

It provides a comprehensive derivation of domain wall conditions from ten dimensions and relates them to four-dimensional effective descriptions, including brane source restrictions.

Findings

Derived general conditions for N=1 supersymmetric domain walls from ten dimensions.

Connected ten-dimensional equations to four-dimensional effective theories.

Showed how supersymmetry constrains brane source locations.

Abstract

We write down the general conditions for N=1 supersymmetric four-dimensional domain walls, deriving them from a ten-dimensional point of view using generalized complex geometry. In cases where the compactification allows for a truncation to a finite number of fields, we make contact with a four-dimensional effective description. In the context of the AdS/CFT correspondence, the equations can be applied to renormalization-group flows of three-dimensional field theories. We allow for the presence of explicit brane sources and show how supersymmetry restricts their location in a natural way.