Flat BPS Domain Walls on 2d K\"ahler-Ricci Soliton

TL;DR

This paper explores flat BPS domain walls in 4d N=1 supergravity with a scalar field on a 2d K"ahler manifold evolving under Ricci flow, analyzing their equations, potentials, and vacua in relation to AdS/CFT.

Contribution

It introduces the deformation of BPS equations and scalar potential driven by K"ahler-Ricci flow in supergravity models.

Findings

BPS equations deform with K"ahler-Ricci soliton parameter

Existence of Lorentz invariant vacua confirmed via RG flows

Connections to AdS/CFT correspondence established

Abstract

In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d K\"ahler manifolds satisfying a K\"ahler-Ricci flow equation. We find that BPS equations and the scalar potential deform with respect to the real parameter related to the K\"ahler-Ricci soliton. In addition, the analysis using gradient and renormalization group flows are carried out to ensure the existence of Lorentz invariant vacua related to Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence.