Holography and renormalization in Lorentzian signature

Albion Lawrence*, Amit Sever

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


De Boer et. al. have found an asymptotic equivalence between the Hamilton-Jacobi equations for supergravity in (d+1)-dimensional asymptotic anti-de Sitter space, and the Callan-Symanzik equations for the dual d-dimensional perturbed conformal field theory. We discuss this correspondence in Lorentzian signature. We construct a gravitational dual of the generating function of correlation functions between initial and final states, in accordance with the construction of Marolf, and find a class of states for which the result has a classical supergravity limit. We show how the data specifying the full set of solutions to the second-order supergravity equations of motion are described in the field theory, despite the first-order nature of the renormalization group equations for the running couplings: one must specify both the couplings and the states, and the latter affects the solutions to the Callan-Symanzik equations.

Original languageEnglish
Article number013
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2006
Externally publishedYes


  • AdS-CFT Correspondence
  • Renormalization Group


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