Universality of Sparse $d>2$ Conformal Field Theory at Large $N$

TL;DR

This paper establishes precise conditions under which large N conformal field theories in dimensions greater than two exhibit universal thermodynamic behavior and an extended Cardy regime, aligning with Einstein gravity duals.

Contribution

It derives necessary and sufficient criteria for universality and extended Cardy behavior in higher-dimensional large N CFTs, and analyzes symmetric orbifold theories in this context.

Findings

Conditions for universal free energy in large N CFTs

Extended validity of higher-dimensional Cardy formula

Symmetric orbifold theories require universal vacuum energy

Abstract

We derive necessary and sufficient conditions for large $N$ conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula. These constraints are much tighter than in two dimensions and must be satisfied by any conformal field theory dual to Einstein gravity. We construct and analyze symmetric product orbifold theories on $\mathbb{T}^d$ and show that they only realize the necessary phase structure and extended range of validity if the seed theory is assumed to have a universal vacuum energy.