April, 1999 | D. Z. Freedman, S. S. Gubser, K. Pilch and N. P. Warner
The paper explores the renormalization group (RG) flow in $\mathcal{N} = 4$ super-Yang-Mills theory, which is broken to an $\mathcal{N} = 1$ theory by adding a mass term for one of the three adjoint chiral superfields. This flow is described by a kink solution in five-dimensional $\mathcal{N} = 8$ gauged supergravity, which interpolates between an anti-de Sitter (AdS) region with maximal supersymmetry and an interior AdS region with one-quarter supersymmetry. The authors derive first-order equations for this kink solution and interpret it as a RG flow in the $\mathcal{N} = 4$ theory. They establish a detailed correspondence between the fields in the bulk supergravity and composite operators in the infrared field theory, and show that the truncation used to find the reduced symmetry critical point can be extended to a new $\mathcal{N} = 4$ gauged supergravity theory holographically dual to a sector of $\mathcal{N} = 2$ gauge theories based on quiver diagrams. The paper also discusses general properties of the supergravity kinks, including the construction of a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. This c-function coincides with the trace anomaly coefficients of the holographically related field theory in the limits where conformal invariance is recovered.The paper explores the renormalization group (RG) flow in $\mathcal{N} = 4$ super-Yang-Mills theory, which is broken to an $\mathcal{N} = 1$ theory by adding a mass term for one of the three adjoint chiral superfields. This flow is described by a kink solution in five-dimensional $\mathcal{N} = 8$ gauged supergravity, which interpolates between an anti-de Sitter (AdS) region with maximal supersymmetry and an interior AdS region with one-quarter supersymmetry. The authors derive first-order equations for this kink solution and interpret it as a RG flow in the $\mathcal{N} = 4$ theory. They establish a detailed correspondence between the fields in the bulk supergravity and composite operators in the infrared field theory, and show that the truncation used to find the reduced symmetry critical point can be extended to a new $\mathcal{N} = 4$ gauged supergravity theory holographically dual to a sector of $\mathcal{N} = 2$ gauge theories based on quiver diagrams. The paper also discusses general properties of the supergravity kinks, including the construction of a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. This c-function coincides with the trace anomaly coefficients of the holographically related field theory in the limits where conformal invariance is recovered.