Renormalization Group Flows from Five-Dimensional Supergravity

TL;DR

This paper reviews how five-dimensional gauged supergravity models can describe renormalization group flows and fixed points in the context of the AdS/CFT correspondence, aligning with field theory results.

Contribution

It demonstrates the use of supergravity to model RG flows, including supersymmetric fixed points and Coulomb branch flows, with a new supergravity inspired c-function and c-theorem.

Findings

Supergravity flows match field theory results.

Identification of a supersymmetric IR fixed point.

Proposal of a supergravity c-function and c-theorem.

Abstract

The use of gauged ${\cal N} = 8$ supergravity as a tool in studying the AdS/CFT correspondence for ${\cal N} = 4$ Yang-Mills theory is reviewed. The supergravity potential implies a non-trivial, supersymmetric IR fixed point, and the flow to this fixed point is described in terms of a supergravity kink. The results agree perfectly with earlier, independent field theory results. A supergravity inspired $c$-function, and corresponding $c$-theorem is discussed for general flows, and the simplified form for supersymmetric flows is also given. Flows along the Coulomb branch of the Yang-Mills theory are also described from the five-dimensional perspective.