Free partition functions and an averaged holographic duality

Understand

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.