Topological closed-string interpretation of Chern-Simons theory

Details Topological closed-string interpretation of Chern-Simons theory Topological closed-string interpretation of Chern-Simons theory

1993-05-24

arxiv.org/abs/hep-th/9305115v2

Phys.Rev.Lett.71:1295-1298,1993

Physics

High Energy Physics

High Energy Physics - Theory

6 pages, iassns-hep-93-30 (title change, omitted refs. added, two sign errors corrected, no significant change)

Scientific paper

10.1103/PhysRevLett.71.1295

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.

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