Holographic renormalization of cascading gauge theories

TL;DR

The paper provides a concrete holographic renormalization of cascading gauge theories by truncating the dual 10D IIB background to a five-dimensional system of the metric plus four scalar fields. It constructs local counter-terms (with a minimal-subtraction scheme) to render all relevant one-point functions finite, including the conformal anomaly, and analyzes ambiguities that arise in curved space. At finite temperature, the renormalized stress tensor yields thermodynamics compatible with a running effective degree of freedom K_eff(T) ∝ ln^2(T/Λ), reconciling finite correlators with the cascade’s infinite UV content. The work lays groundwork for extending holographic renormalization to more general backgrounds and higher-point functions in cascading theories.

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.