Four-dimensional BF theory as a topological quantum field theory |
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Authors: | John C Baez |
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Institution: | (1) Department of Mathematics, University of California, 92521 Riverside, CA, U.S.A. |
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Abstract: | Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G=GL(4, ) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of four-manifolds. |
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Keywords: | 57N13 81T43 83C45 |
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