Three-dimensional AdS gravity and extremal CFTs at c=8m

TL;DR

This paper explores the extension of Witten's duality between extremal self-dual CFTs and 3D AdS gravity to central charges that are multiples of 8, providing explicit calculations up to c=88.

Contribution

It extends the duality framework to higher central charges and computes partition functions and state degeneracies for these theories.

Findings

Genus one partition functions computed up to c=88

Exact and approximate degeneracy formulas provided

Genus two partition functions calculated up to c=40

Abstract

We note that Witten's proposed duality between extremal c=24k CFTs and three-dimensional anti-de Sitter gravity may possibly be extended to central charges that are multiples of 8, for which extremal self-dual CFTs are known to exist up to c=40. All CFTs of this type with central charge 24 or higher, provided that they exist, have the required mass gap and may serve as candidate duals to three-dimensional gravity at the corresponding values of the cosmological constant. Here, we compute the genus one partition function of these theories up to c=88, we give exact and approximate formulas for the degeneracies of states, and we determine the genus two partition functions of the theories up to c=40.