TY - JOUR

T1 - Holography and renormalization in Lorentzian signature

AU - Lawrence, Albion

AU - Sever, Amit

PY - 2006/10/1

Y1 - 2006/10/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Renormalization Group

UR - http://www.scopus.com/inward/record.url?scp=33846160989&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2006/10/013

DO - 10.1088/1126-6708/2006/10/013

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AN - SCOPUS:33846160989

SN - 1029-8479

VL - 2006

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 013

ER -