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Topological closed-string interpretation of Chern-Simons theory. (English) Zbl 0972.81596
Summary: The exact free energy of SU\((N)\) Chern-Simons theory at level \(k\) is expanded in powers of \((N+k)^{-2}\). 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.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
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