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Article Dans Une Revue Nuclear Physics B Année : 2014

Path-integral invariants in abelian Chern-Simons theory

Résumé

We consider the U(1) Chern-Simons gauge theory defined in a general closed oriented 3-manifold M ; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1)U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.
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Dates et versions

hal-00973733 , version 1 (04-04-2014)

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Guadagnini Enore, Thuillier Frank. Path-integral invariants in abelian Chern-Simons theory. Nuclear Physics B, 2014, 882, pp.450-484. ⟨10.1016/j.nuclphysb.2014.03.009⟩. ⟨hal-00973733⟩
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