Chern-Simons theory on a lattice and a new description of 3-manifolds invariants

Details Chern-Simons theory on a lattice and a new description of 3-manifolds invariants Chern-Simons theory on a lattice and a new description of 3-manifolds invariants

1995-09-19

arxiv.org/abs/q-alg/9509020v1

Mathematics

Quantum Algebra

45 pages in Latex (figures are in an auxilliary compressed file)

Scientific paper

A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice gauge theory based on a quantum group. After a generalization of the formalism of q-deformed gauge theory to the case of root of unity, we compute explicitely the correlation functions associated to Wilson loops (and more generally to graphs) on a surface with punctures, which are the interesting quantity in the study of moduli space. We then give a new description of Chern-Simons three manifolds invariants based on a description in terms of the mapping class group of a surface. At last we introduce a three dimensional lattice gauge theory based on a quantum group which is a lattice regularization of Chern-Simons theory.

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