Renormalization group flows from holography-supersymmetry and a c-theorem

D. Z. Freedman, S. S. Gubser, K. Pilch, N. P. Warner

Research output: Contribution to journalArticlepeer-review

454 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1-55
Number of pages55
JournalAdvances in Theoretical and Mathematical Physics
Issue number2
StatePublished - Mar 1999

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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