Towards Holographic Renormalization of Fake Supergravity

TL;DR

This paper extends holographic renormalization techniques to non-AdS backgrounds with running couplings, providing a method to compute renormalized two-point functions in fake supergravity models like Klebanov-Strassler.

Contribution

It introduces a general recipe for holographic renormalization in non-AdS backgrounds, applicable to fake supergravity theories, and verifies consistency with known AdS results.

Findings

Recipe for calculating renormalized two-point functions using gauge-invariant variables.

Method successfully reproduces known results in asymptotically AdS backgrounds.

Provides insights into renormalized vacuum expectation values in non-AdS holography.

Abstract

A step is made towards generalizing the method of holographic renormalization to backgrounds which are not asymptotically AdS, corresponding to a dual gauge theory which has logarithmically running couplings even in the ultraviolet. A prime example is the background of Klebanov-Strassler (KS). In particular, a recipe is given how to calculate renormalized two-point functions for the operators dual to the bulk scalars. The recipe makes use of gauge-invariant variables for the fluctuations around the background and works for any bulk theory of the fake supergravity type. It elegantly incorporates the renormalization scheme dependence of local terms in the correlators. Before applying the method to the KS theory, it is verified that known results in asymptotically AdS backgrounds are reproduced. Finally, some comments on the calculation of renormalized vacuum expectation values are made.