Domain walls and flow equations in supergravity

TL;DR

This paper explores domain wall solutions in supergravity, focusing on flow equations, critical points, and conditions for localizing gravity, with implications for brane worlds and holographic RG flows.

Contribution

It derives first order flow equations as Bogomol'nyi bounds and analyzes superpotential types and supersymmetry constraints relevant for gravity localization.

Findings

Derived first order flow equations as Bogomol'nyi bounds

Identified superpotential types for critical points and gravity trapping

Provided examples of supersymmetric flows in supergravity

Abstract

Domain wall solutions have attracted much attention due to their relevance for brane world scenarios and the holographic RG flow. In this talk I discuss the following aspects for these applications: (i) derivation of the first order flow equations as Bogomol'nyi bound; (ii) different types of critical points of the superpotential; (iii) the superpotential needed to localize gravity; (iv) the constraints imposed by supersymmetry including an example for an $N$=1 flow and finally (v) sources and exponential trapping of gravity.