String Universality for Permutation Orbifolds

TL;DR

The paper tests the String Universality conjecture within AdS$_3$/CFT$_2$ by analyzing permutation orbifolds $\\mathcal{C}_{G_N}=\\mathcal{C}^{\\otimes N}/G_N$ with $G_N\\subseteq S_N$. It proves a density-of-states conjecture for these large-$N$ CFTs, identifies which permutation groups yield a well-defined large-$N$ limit, and shows that their holographic duals possess a Hagedorn (string-like) spectrum in the large-$N$ limit. The untwisted sector already imposes strong, nonlocal constraints on the bulk, while twisted sectors—driven by long cycles in $G_N$—drive the Hagedorn growth, indicating the dual must be a string theory rather than a local QFT. Collectively, the results establish that, within this landscape, any semi-classical theory of quantum gravity emerges as a string theory when dual to permutation orbifolds.

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.