Partition functions and double-trace deformations in AdS/CFT

TL;DR

This paper investigates how double-trace deformations affect the partition function and conformal anomaly in AdS/CFT, demonstrating exact equality of partition functions and exploring UV-IR effects beyond classical supergravity.

Contribution

It provides a comprehensive analysis confirming the equivalence of bulk and boundary computations for partition functions under double-trace deformations, including effects on anomalies and UV-IR mixing.

Findings

Exact equality of regularized partition functions in bulk and boundary

Correction to conformal anomaly for even dimensions

Identification of UV-IR mixing effects in the duality

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.