Harmonic analysis of 2d CFT partition functions

A bstract We apply the theory of harmonic analysis on fundamental domain SL(2 , ?) to partition functions two-dimensional conformal field theories. decompose function c free bosons a Narain lattice into eigenfunctions Laplacian worldsheet moduli space ?/SL(2 ?), and target O ( c, ; ?)\ ?)/ ) × ). This decomposition manifests certain properties theories ensemble averages thereof. extend application spectral general theories, explore its meaning in connection AdS 3 gravity. An implication is that local operator spectrum fully determined by subset degeneracies.