Abstract
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.
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Communicated by A. Jaffe
The first author is supported by NSF grant DMS-8805684, an Alfred P. Sloan Research Fellowship, and a Presidential Young Investigators award. The second author is supported by NSF grant DMS-8902153
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Freed, D.S., Gompf, R.E. Computer calculation of Witten's 3-manifold invariant. Commun.Math. Phys. 141, 79–117 (1991). https://doi.org/10.1007/BF02100006
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DOI: https://doi.org/10.1007/BF02100006