Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT

By Ioannis Papadimitriou. 2007

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We present a general and systematic treatment of multi-trace deformations in the AdS/CFT correspondence in the large N limit, pointing out and clarifying subtleties relating to the formulation of the boundary value problem on a conformal boundary. We then apply this method to study multi-trace deformations in the presence of a scalar VEV, which requires the coupling to gravity to be taken into account. We show that supergravity solutions subject to `mixed' boundary conditions are in one-to-one correspondence with critical points of the holographic effective action of the dual theory in the presence of a multi-trace deformation, and we find a number of new exact analytic solutions involving a minimally or conformally coupled scalar field satisfying `mixed' boundary conditions. These include the generalization to any dimension of the instanton solution recently found in hep-th/0611315. Finally, we provide a systematic method for computing the holographic effective action in the presence of a multi-trace deformation in a derivative expansion away from the conformal vacuum using Hamilton-Jacobi theory. Requiring that this effective action exists and is bounded from below reproduces recent results on the stability of the AdS vacuum in the presence of `mixed' boundary conditions.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0cb183ef30d4e820af70e2a7a5525a447eb3bf9c

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Citations in the corpus

AdS2 holographic dictionary (2016, background): “Such solutions are a characteristic property of conformally coupled scalars and exist even in higher dimensions [62, 63].”