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

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.

32 pages + appendices

References in corpus (5)

• Holography from Conformal Field Theory
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Permutation orbifolds and holography
• Black holes and universality classes of critical points

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