4-Dimensional BF Theory as a Topological Quantum Field Theory

Details 4-Dimensional BF Theory as a Topological Quantum Field Theory 4-Dimensional BF Theory as a Topological Quantum Field Theory

1995-07-10

arxiv.org/abs/q-alg/9507006v1

Lett.Math.Phys. 38 (1996) 129-143

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages in LaTeX

Scientific paper

10.1007/BF00398315

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that 4-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,R) 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 4-manifolds.

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