BPS Domain Walls and Vacuum Structure of N=1 Supergravity Coupled to a Chiral Multiplet

TL;DR

This paper investigates BPS domain walls and vacuum structures in N=1 supergravity with a chiral multiplet, revealing stability conditions and the limitations of gradient flows near potential maxima.

Contribution

It provides a detailed analysis of BPS domain walls, vacuum critical points, and the stability of gradient flows influenced by superpotential and Kähler geometry.

Findings

Gradient flows are unstable near local maxima of the scalar potential.

Stable gradient flows occur around local minima and saddles.

RG flow analysis shows gradient flows may not exist in the infrared region.

Abstract

We study BPS domain walls of N=1 supergravity coupled to a chiral multiplet and their Lorentz invariant vacua which can be viewed as critical points of BPS equations and the scalar potential. Supersymmetry further implies that gradient flows of BPS equations controlled by a holomorphic superpotential and the Kaehler geometry are unstable near local maximum of the scalar potential, whereas they are stable around local minimum and saddles of the scalar potential. However, the analysis using RG flows shows that such gradient flows do not always exist particularly in infrared region.