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Register a new userRenormalization Group Flows from Five-Dimensional Supergravity
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N.P. Warner
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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.
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We consider N=1 supersymmetric renormalization group flows of N=4 Yang-Mills theory from the perspective of ten-dimensional IIB supergravity. We explicitly construct the complete ten-dimensional lift of the flow in which exactly one chiral superfield becomes massive (the LS flow). We also examine the ten-dimensional metric and dilaton configurations for the ``super-QCD flow (the GPPZ flow) in which all chiral superfields become massive. We show that the latter flow generically gives rise to a dielectric 7-brane in the infra-red, but the solution contains a singularity that may be interpreted as a ``duality averaged ring distribution of 5-branes wrapped on S^2. At special values of the parameters the singularity simplifies to a pair of S-dual branes with (p,q) charge (1,pm 1).
We present a projective superspace formulation for matter-coupled simple supergravity in five dimensions. Our starting point is the superspace realization for the minimal supergravity multiplet proposed by Howe in 1981. We introduce various off-shell supermultiplets (i.e. hypermultiplets, tensor and vector multiplets) that describe matter fields coupled to supergravity. A projective-invariant action principle is given, and specific dynamical systems are constructed including supersymmetric nonlinear sigma-models. We believe that this approach can be extended to other supergravity theories with eight supercharges in $Dleq 6$ space-time dimensions, including the important case of 4D N=2 supergravity.
We consider line defects in d-dimensional Conformal Field Theories (CFTs). The ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. We show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We demonstrate our results in a flow between Wilson loops in 4 dimensions.
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.
We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is non-Abelian, and leads to a positive-definite universal contribution to the S-matrix of 2->2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.
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