Partition functions and double-trace deformations in AdS/CFT

TL;DR

The paper tests AdS/CFT at subleading order by analyzing how a relevant double-trace deformation affects the CFT partition function and the AdS_{d+1} bulk via one-loop corrections. The authors compute the bulk difference between $Δ_+$ and $Δ_-$ quantizations and the boundary determinant induced by the Hubbard-Stratonovich flow, both in dimensional regularization, and show exact agreement of dimensionally regularized quantities for all $d$. In odd dimensions the effect is a finite renormalized partition-function correction with no anomaly, while in even dimensions a conformal anomaly appears and requires careful IR–UV cancellation between volume and effective potential pieces. The results provide a clean, regulator-consistent test of AdS/CFT beyond classical gravity and offer a bridge to conformal geometry through GJMS-type determinant structures.

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.