Higher Dimensional Curved Domain Walls on K\"ahler Surfaces

TL;DR

This paper investigates curved BPS-like domain walls in higher-dimensional gravity coupled with scalars on K"ahler surfaces, establishing conditions for solutions, analyzing vacuum stability, and exploring RG flow behavior.

Contribution

It introduces a specific form of fake superpotential depending on K"ahler potential and holomorphic functions, proving the uniqueness of BPS-like solutions in this setting.

Findings

Existence of unique local solutions for BPS-like equations.

Analysis of vacuum stability and structure.

Investigation of domain wall behavior in UV and IR regions.

Abstract

In this paper we study some aspects of curved BPS-like domain walls in higher dimensional gravity theory coupled to scalars where the scalars span a complex K\"ahler surface with scalar potential turned on. Assuming that a fake superpotential has a special form which depends on K\"ahler potential and a holomorphic function, we prove that BPS-like equations have a local unique solution. Then, we analyze the vacuum structure of the theory including their stability using dynamical system and their existence in ultraviolet-infrared regions using renormalization group flow.