Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants

Details Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants

2002-07-10

arxiv.org/abs/hep-th/0207096v4

Commun.Math.Phys. 253 (2004) 25-49

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, JHEP style, typos corrected, some improvements in section 5.2, references added

Scientific paper

10.1007/s00220-004-1194-4

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some previous results of Lawrence and Rozansky, the Chern-Simons partition function with arbitrary simply-laced group for these spaces is written in terms of matrix integrals. The analysis of the perturbative expansion amounts to the evaluation of averages in a Gaussian ensemble of random matrices. As a result, explicit expressions for the universal perturbative invariants of Seifert homology spheres up to order five are presented.

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