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Topological closed-string interpretation of Chern-Simons theory

1993; American Physical Society; Volume: 71; Issue: 9 Linguagem: Inglês

10.1103/physrevlett.71.1295

1092-0145

Vipul Periwal,

Noncommutative and Quantum Gravity Theories

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.