Holographic renormalization of cascading gauge theories

TL;DR

This paper develops a holographic renormalization procedure for cascading gauge theories, enabling finite correlation functions and stress tensor calculations despite the theories' infinite degrees of freedom.

Contribution

It introduces a finite holographic renormalization scheme for cascading gauge theories, including explicit counter-terms and stress tensor computations.

Findings

Finite one-point functions obtained despite infinite degrees of freedom

Explicit form of counter-terms for the dual gravitational backgrounds

Consistent stress tensor calculations at high temperature

Abstract

We perform a holographic renormalization of cascading gauge theories. Specifically, we find the counter-terms that need to be added to the gravitational action of the backgrounds dual to the cascading theory of Klebanov and Tseytlin, compactified on an arbitrary four-manifold, in order to obtain finite correlation functions (with a limited set of sources). We show that it is possible to truncate the action for deformations of this background to a five dimensional system coupling together the metric and four scalar fields. Somewhat surprisingly, despite the fact that these theories involve an infinite number of high-energy degrees of freedom, we find finite answers for all one-point functions (including the conformal anomaly). We compute explicitly the renormalized stress tensor for the cascading gauge theories at high temperature and show how our finite answers are consistent with the infinite number of degrees of freedom. Finally, we discuss ambiguities appearing in the holographic renormalization we propose for the cascading gauge theories; our finite results for the one-point functions have some ambiguities in curved space (including the conformal anomaly) but not in flat space.