Partition functions and double-trace deformations in AdS/CFT

Abstract

We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each other: bulk and boundary computations, as well as their formal identity. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuational determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.

18 pages, uses JHEP3.cls. Published JHEP version

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• AdS/CFT correspondence and Geometry
• Functional determinants for radial operators
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions

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