Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem

TL;DR

This paper constructs supersymmetric holographic RG flow solutions in five-dimensional supergravity, revealing a c-theorem and connections to N=4 and N=2 gauge theories through detailed bulk-boundary correspondence.

Contribution

It provides explicit first order equations for supersymmetric kink solutions and extends the holographic framework to new supergravity theories and RG flow analyses.

Findings

Constructed supersymmetric kink solutions in 5D supergravity.

Established a monotonic c-function consistent with energy conditions.

Linked bulk supergravity fields to operators in IR gauge theories.

Abstract

We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For even-dimensional boundaries, the c-function coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.