String Universality for Permutation Orbifolds

TL;DR

This paper proves a conjecture about the density of states in 2D CFTs orbifolded by permutation groups, showing they have a Hagedorn spectrum and are likely string theories in the context of AdS_3 holography.

Contribution

It characterizes permutation groups leading to well-defined large N limits in 2D CFTs and demonstrates their holographic duals exhibit string-like Hagedorn spectra.

Findings

Permutation orbifolds with certain groups have well-defined large N limits.

Holographic duals of these orbifolds exhibit Hagedorn spectra.

Supports the idea that all semi-classical quantum gravity theories in AdS_3 are string theories.

Abstract

The hypothesis that every theory of quantum gravity in AdS_3 is a dimensional reduction of string/M-theory leads to a natural conjecture for the density of states of two dimensional CFTs with a large central charge limit. We prove this conjecture for 2D CFTs which are orbifolds by permutation groups. In particular, we characterize those permutation groups which give CFTs with well-defined large N limits and can thus serve as holographic duals to bulk gravity theories in AdS_3. We then show that the holographic dual of a permutation orbifold will have a Hagedorn spectrum in the large N limit. This is evidence that, within this landscape, every theory of quantum gravity with a semi-classical limit is a string theory.