Averaging over moduli in deformed WZW models

WZW models live on a moduli space parameterized by current-current deformations. The defines an ensemble of conformal field theories, which generically have $N$ abelian conserved currents and central charge $c > N$. We calculate the average partition function show that it can be interpreted as sum over 3-manifolds. This suggests ensemble-averaged theory has holographic dual, generalizing recent results Narain CFTs. bulk theory, at perturbative level, is identified $U(1)^{2N}$ Chern-Simons coupled to additional matter fields. From mathematical perspective, our principal result Siegel-Weil formula for characters affine Lie algebra.