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

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

1999-04-03

arxiv.org/abs/hep-th/9904017v3

Adv.Theor.Math.Phys.3:363-417,1999

Physics

High Energy Physics

High Energy Physics - Theory

56 pages, three figures, harvmac. v2: improved referencing, corrected discussion of energy conditions. v3: one more reference

Scientific paper

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.

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