Short distance properties of cascading gauge theories

TL;DR

This paper investigates the short-distance behavior of cascading gauge theories using holographic duality, demonstrating their renormalizability and the expected scaling of correlation functions with energy.

Contribution

It proves the holographic renormalizability of cascading gauge theories and characterizes their correlation functions' scaling at high energies.

Findings

Correlation functions have only analytic UV divergences.

Correlation functions scale as N_{eff}^{2-n} with N_{eff} ~ ln(k/Λ).

Cascading gauge theories are confirmed as renormalizable with a logarithmically increasing degrees of freedom.

Abstract

We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a tree-level computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that n-point correlation functions of properly normalized operators have the expected scaling in the semi-classical gravity (large N) limit: they scale as N_{eff}^{2-n} with N_{eff} proportional to ln(k/Lambda) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable four-dimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy.