Topological quantum field theories, moduli spaces, and flat gauge connections
- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (USA)
We show how to construct a topological quantum field theory which corresponds to a given moduli space. We apply this method to the case of flat gauge connections defined over a Riemann surface and discuss its relations with the Chern-Simons theory and conformal field theory. Geometrical properties are invoked to prove that the observables of those theories are not trivial. The case of the SO(2,1) group is separately discussed. A topological field theory is linked to the moduli space of self-dual'' connections over Riemann surfaces. Another relation between the Chern-Simons theory and topological quantum field theory in three dimensions is established. We present the theory which corresponds to three-dimensional gravity. Expressions for the Casson invariants are given. Possible generalizations are briefly discussed.
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6227553
- Journal Information:
- Physical Review, D (Particles Fields); (USA), Vol. 42:6; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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