Free partition functions and an averaged holographic duality

TL;DR

This paper investigates the averaged properties of free bosonic 2D CFTs, revealing a connection to 3D topologies and proposing a novel holographic duality involving an exotic 3D gravity theory with specific symmetries.

Contribution

It introduces an ensemble average of free CFTs via Narain moduli integration and conjectures a new holographic duality to a 3D gravity theory with $U(1)^c imes U(1)^c$ symmetry.

Findings

Averaged partition function interpreted as sum over 3D topologies

Constraints on spectral gap for small central charge

Construction of Narain compactifications with large spectral gap

Abstract

We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with $U(1)^c \times U(1)^c$ symmetry and a composite boundary graviton. Additionally, for small central charge $c$, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.