Path-integral invariants in abelian Chern–Simons theory

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...

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Bibliographic Details
Published in:Nuclear physics. B 2014-05, Vol.882, p.450-484
Main Authors: Guadagnini, E., Thuillier, F.
Format: Article
Language:English
Subjects:
High Energy Physics - Theory
Mathematical Physics
Mathematics
Physics
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Summary: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) 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.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2014.03.009