Partition functions and double-trace deformations in AdS/CFT

By D. E. D'iaz, H. Dorn. 2007

147 citations recorded by the source corpus.

We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFTd at large N and its dual picture in AdSd+1. Three complementary previous results are brought into full agreement with each other: bulk [1] and boundary [2] computations, as well as their formal identity [3]. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuation 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.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9d7eee6be206d44c57efc1d796d58fe3ec0dcd25

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Citations in the corpus

A one-loop test of quantum supergravity (2012, background): “7) The regularized volume of AdS4 can be calculated by standard procedure (see for example [33, 6]) but since this forms an integral part of our analysis, we shall review it here.”
Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “That a coefficient in Ā should have 4-th order polynomial dependence on ∆ follows already from the results for a general massive 5d scalar in euclidean AdS5 with boundary S 4 [9, 10, 1].”
Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT (2007, background): “W e presenta generaland system atic treatm entofm ulti-trace deform ations in the AdS/CFT correspondence in the large N lim it,pointing outand clarifying subtletiesrelating to the form ulation ofthe boundary value problem on a conform alboundary.”
Notes on the complex Sachdev-Ye-Kitaev model (2019, methodology): “We note that this procedure is similar to that used to compute the influence of double trace operators on the free energy in the AdS/CFT correspondence [40–45].”
One loop tests of higher spin AdS/CFT (2013, background): “This procedure gives a result in agreement with the difference F∆+ − F∆− computed using different methods [25,30,33].”
AdS description of induced higher-spin gauge theory (2013, methodology): “The s = 0 calculation has been performed in [10, 11], and as a warmup we begin by reviewing that computation.”