CFT(4) Partition Functions and the Heat Kernel on AdS(5)

TL;DR

This paper reformulates the partition function of any 4D conformal field theory into a heat kernel form related to the dual string spectrum on AdS(5), providing a general approach applicable to various dimensions.

Contribution

It introduces a method to express 4D CFT partition functions as heat kernels linked to dual string spectra, applicable across different dimensions.

Findings

Partition function reorganized into heat kernel form.

Expressed in terms of a convolution of one-particle partition functions.

Method applicable to arbitrary dimensions.

Abstract

We explicitly reorganise the partition function of an arbitrary CFT in four spacetime dimensions into a heat kernel form for the dual string spectrum on AdS(5). On very general grounds, the heat kernel answer can be expressed in terms of a convolution of the one-particle partition function of the four-dimensional CFT. Our methods are general and would apply for arbitrary dimensions, which we comment on.