Topological closed-string interpretation of Chern-Simons theory

The exact free energy of SU(N) Chern-Simons theory at level k is expanded in powers of (N+k${)}^{\mathrm{-}2}$. This expansion keeps rank-level duality manifest, and simplifies as k becomes large, keeping N fixed (or vice versa)—this is the weak-coupling (strong-coupling) limit. With the standard normalization, the free energy on the three-sphere in this limit is shown to be the generating function of the Euler characteristics of the moduli spaces of surfaces of genus g, providing a string interpretation for the perturbative expansion. A similar expansion is found for the three-torus, with differences that shed light on contributions from different spacetime topologies in string theory.