Holographic RG flows on curved manifolds and quantum phase transitions

TL;DR

This paper explores holographic renormalization group flows on curved manifolds, revealing new flows, bouncing behaviors, and quantum phase transitions driven by curvature variations in Einstein-dilaton gravity.

Contribution

It introduces the analysis of holographic RG flows on curved spaces with a general dilaton potential, discovering new finite curvature flows and quantum phase transitions.

Findings

Discovery of new RG flows at finite curvature

Persistence of bouncing flows with sign-changing beta functions

Identification of quantum first-order phase transitions triggered by curvature variations

Abstract

Holographic RG flows dual to QFTs on maximally symmetric curved manifolds (dS$_d$, AdS$_d$, and $S^d$) are considered in the framework of Einstein-dilaton gravity in $d+1$ dimensions. A general dilaton potential is used and the flows are driven by a scalar relevant operator. The general properties of such flows are analyzed and the UV and IR asymptotics computed. New RG flows can appear at finite curvature which do not have a zero curvature counterpart. The so-called 'bouncing flows', where the $\beta$-function has a branch cut at which it changes sign, are found to persist at finite curvature. Novel quantum first-order phase transitions are found, triggered by a variation in the $d$-dimensional curvature in theories allowing multiple ground states.