Renormalization Group Flows from Five-Dimensional Supergravity

TL;DR

This work demonstrates how five-dimensional gauged ${\cal N}=8$ supergravity can model non-conformal RG flows of ${\rm N}=4$ SYM via holography. By analyzing kink solutions governed by a superpotential $W$, it identifies a non-trivial supersymmetric IR fixed point that matches Leigh–Strassler-type deformations in the field theory and establishes a gravity-based ${\rm c}$-function that decreases along RG flows and becomes the central charge at fixed points. The study also clarifies the role of embedding/truncation, the field/state/operator dictionary, and the interpretation of Coulomb-branch flows within the AdS/CFT framework, including the stability criteria set by the Breitenlohner–Freedman bound. Together, these results support the robustness of holographic RG flows and highlight the non-linear structure of the five-dimensional potential in predicting non-perturbative gauge-theory dynamics.

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.