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. e-print archive: http.y/xxx.lanl.gov/abs/hep-th/9904017 *On leave from Department of Physics and Astronomy, USC, Los Angeles, CA 90089 364 RENORMALIZATION GROUP FLOWSWe 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.

Mesons in gauge/gravity duals

“…Other more complicated examples of holographic RG flows exist in the literature [54][55][56][57]. Generically, the more supersymmetry is retained the more checks of their agreement with field theory exist.…”

“…The scalar and gauge field fluctuations are taken to be of the form (a = 8, 9) 56) and can be written as…”

Implications of bulk causality for holography in AdS

“…This tension is balanced in Einstein's equations by the difference in the AdS curvatures on either side of the wall. Very similar solutions occur in string theory examples where a particular mass deformation is added in the boundary gauge theory, so that some reduced supersymmetry is preserved in the region interior to the domain wall and the boundary theory flows in the IR to a conformal theory with a lower central charge [8]. The gravity description of this is essentially the kink solution presented here.…”

“…Therefore we see that for flows from CFT to CFT, the four-dimensional c-theorem [8] is equivalent to our condition.…”

Null deformed domain wall

“…As shown in [26] the inclusion of hypermultiplets is crucial to have BPS Domain walls interpolating between two AdS vacua and consequently to embed the Domain wall solution of [27] (FGPW) in the N = 2 gauged supergravity, as holographic dual to an RG flow from an N = 4 to an N = 1 SYM. In [28] has been proved, while clarifying the relation between Fake [29] and N = 2 gauged supergravity, that curved Domain Walls can be obtained only with hypermultiplets coupled.…”