Holographic RG Flows from Quasi-Topological Gravity

TL;DR

This paper explores holographic RG flows in quasi-topological gravity coupled with scalar matter, deriving explicit beta-functions and anomalies, and analyzing critical phenomena, phase transitions, and the influence of Lovelock couplings.

Contribution

It provides explicit formulas for beta-functions and trace anomalies in holographic duals, analyzing their dependence on superpotential and Lovelock couplings, and studying phase transitions in dual QFTs.

Findings

Derived explicit beta-functions and anomaly functions in holographic duals.

Identified conditions for the validity of the a/c-theorems.

Analyzed phase transitions and critical points in dual QFTs.

Abstract

We investigate the holographic Renormalization Group (RG) flows and the critical phenomena that take place in the $QFT$'s dual to the d-dimensional cubic Quasi-Topological Gravity coupled to scalar matter. The knowledge of the corresponding flat Domain Walls(DWs) solutions, allows us to derive the explicit form of the $QFT$'s beta-functions as well as of the trace anomalies $a(l)$ and $c(l)$-functions in terms of the matter superpotential. As a consequence we are able to determine the complete set of $CFT$ data characterizing the universality classes of the UV and IR critical points and to follow the particular RG evolution of this data. We further analyse the dependence of the critical properties of such dual $QFT$'s on the values of the Lovelock couplings and on the shape of the superpotential. For odd values of $d$, the explicit form of the "a- and c- central charges" as functions of the running coupling constant, enable us to establish the conditions under which the $a/c$-Theorems for their decreasing are valid. The restrictions imposed on the massless Holographic RG flows by the requirements of the positivity of the energy fluxes are derived. The particular case of quartic Higgs-like superpotential is studied in detail. It provides an example of unitary dual $QFT$'s having few $c\ne a$ critical points representing second or infinite order phase transitions. Depending on the range of the values of the coupling constant they exhibit massive and massless phases, described by a chain of distinct DWs solutions sharing common boundaries.