Sphere partition functions and cut-off AdS

TL;DR

The paper develops and tests a generalized TT (trace of the stress-energy tensor) deformation strategy in large-N CFTs across dimensions d=2..6, focusing on sphere partition functions as a precise diagnostic. It demonstrates non-perturbative agreement between field theory flow equations and bulk AdS gravity with a finite radial cut-off, and shows how the flow can be derived from a local Callan-Symanzik framework with curvature-aware regularization. The results hinge on a central quantity ω[r_c] that links holographic stress tensors to TT-flow data, and they are complemented by a Wheeler-DeWitt (mini-superspace) analysis that reproduces the same partition functions up to holographic counterterms. Overall, the work provides a cohesive picture tying finite-cutoff holography, higher-dimensional TT deformations, and quantum gravity constraints, with clear paths for extending to other backgrounds and 1/N corrections.

Abstract

We consider sphere partition functions of TT deformed large N conformal field theories in d=2,3,4,5 and 6 dimensions, computed using the flow equation. These are shown to non-perturbatively match with bulk computations of $AdS_{d+1}$ with a finite radial cut-off. We then demonstrate how the flow equation can be independently derived from a regularization procedure in defining TT operators through a local Callan-Symanzik equation. Finally, we show that the sphere partition functions, modulo bulk-counterterm contributions, can be reproduced from Wheeler-DeWitt wave functions.