N=1 Supergravity BPS Domain Walls on K\"ahler-Ricci Soliton

TL;DR

This paper explores BPS domain walls and vacua in four-dimensional N=1 supergravity with scalar manifolds evolving under K"ahler-Ricci flow, analyzing their geometric and physical properties.

Contribution

It introduces a framework linking K"ahler-Ricci flow to the structure of BPS domain walls and vacua in supergravity, including a specific model with linear superpotential.

Findings

Vacuum manifolds deform under K"ahler-Ricci flow.

Renormalization group analysis determines vacuum stability.

A simple model on U(n) symmetric K"ahler-Ricci orbifolds is discussed.

Abstract

This paper provides a study of some aspects of flat and curved BPS domain walls together with their Lorentz invariant vacua of four dimensional chiral N=1 supergravity. The scalar manifold can be viewed as a one-parameter family of K\"ahler manifolds generated by a K\"ahler-Ricci flow equation. Consequently, a vacuum manifold characterized by $(m,\lambda)$ where $m$ and $\lambda$ are the dimension and the index of the manifold, respectively, does deform with respect to the flow parameter related to the geometric soliton. Moreover, one has to carry out the renormalization group analysis to verify the existence of such a vacuum manifold in the ultraviolet or infrared regions. At the end, we discuss a simple model with linear superpotential on U(n) symmetric K\"ahler-Ricci orbifolds.