RG Fixed Points in Supergravity Duals of 4-d Field Theory and Asymptotically AdS Spaces

TL;DR

This paper supports the conjecture that supergravity solutions with dual AdS regions model the RG flow of 4-d field theories between fixed points, by analyzing scalar two-point functions in asymptotically AdS spaces.

Contribution

It demonstrates that scalar two-point functions depend only on the UV or IR regions in the respective limits, reinforcing the supergravity dual description of RG flows.

Findings

Two-point functions depend solely on the UV or IR asymptotic regions.

Results are consistent with the radial coordinate as an energy scale.

Supports the analogy of the supergravity RG flow with the Callan-Symanzik equation.

Abstract

Recently, it has been conjectured that supergravity solutions with two asymptotically AdS regions describe the RG flow of a 4-d field theory from a UV fixed point to an interacting IR fixed point. In this paper we lend support to this conjecture by showing that, in the UV (IR) limit, the two-point function of a minimally-coupled scalar field depends only on the UV (IR) region of the metric, asymptotic to AdS_5. This result is consistent with the interpretation of the radial coordinate of Anti de Sitter space as an energy scale, and it may provide an analog of the Callan-Symanzik equation for supergravity duals of strongly coupled field theories.