Exact holographic RG flows and the $A_{1}\times A_{1}$ Toda chain

TL;DR

This paper constructs exact analytic solutions in Einstein-dilaton gravity using Toda chain integrability, revealing novel holographic RG flows between AdS and hyperscaling violating geometries, including finite temperature black branes.

Contribution

It introduces a method to find exact solutions for Einstein-dilaton systems via Toda chain integrability, enabling detailed holographic RG flow analysis.

Findings

Exact solutions interpolating between AdS and hyperscaling geometries

Analytic black brane solutions at finite temperature

Insights into holographic RG flows and boundary interpretations

Abstract

We construct analytic solutions of Einstein gravity coupled to a dilaton field with a potential given by a sum of two exponentials, by rewriting the equations of motion in terms of an integrable Toda chain. These solutions can be interpreted as domain walls interpolating between different asymptotics, and as such they can have interesting applications in holography. In some cases, we can construct a solution which interpolates between an AdS fixed point in the UV limit and a hyperscaling violating boundary in the IR region. We also find analytic black brane solutions at finite temperature. We discuss the properties of the solutions and the interpretation in terms of RG flow.