Renormalization group flows from holography: Supersymmetry and a $c$-theorem

Abstract

We obtain first order equations that determine a super symmetric kink solution in five-dimensional Af = 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 J\f = 4 super-Yang-Mills theory broken to an Af = 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 Af = 4 gauged supergravity theory holographically dual to a sector of Af = 2 gauge theories based on quiver diagrams.