# Sphere partition functions and cut-off AdS

## TL;DR

This paper explores the relationship between sphere partition functions of TT deformed large N conformal field theories across multiple dimensions and their dual bulk AdS computations with a finite cutoff, revealing new insights into holographic dualities.

## Contribution

It demonstrates a non-perturbative match between boundary sphere partition functions and bulk AdS calculations with a cutoff, and derives the flow equation from a local Callan-Symanzik perspective.

## Key findings

- Non-perturbative match of sphere partition functions with bulk AdS with cutoff
- Flow equation derivation from local Callan-Symanzik equation
- Reproduction of partition functions from Wheeler-DeWitt wave functions

## 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.