  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.
