Gravitational Stability and Renormalization-Group Flow

TL;DR

This work develops a model-independent framework for gravitational stability and holographic RG flows using dilaton domain walls in D-dimensional gravity. By expressing the scalar potential through a superpotential $w(φ)$, it derives first-order Bogomol'nyi equations that describe BPS domain walls andachieve AdS vacua stability via the BF bound, tying wall solutions to Killing spinors. It introduces a holographic c-function that monotonically decreases along RG flows, linking bulk dynamics to the dual field theory's RG trajectories. The paper provides explicit 1/2-SUSY domain-wall solutions in D=7 and D=6 supergravities and a mathematical Weierstrass-function example, illustrating the general solution structure and the rich landscape of holographic RG flows.

Abstract

First-order `Bogomol'nyi' equations are found for dilaton domain walls of D-dimensional gravity with the general dilaton potential admitting a stable anti-de Sitter vacuum. Implications for renormalization group flow in the holographically dual field theory are discussed.