BF Theories and 2-knots

Details BF Theories and 2-knots BF Theories and 2-knots

1994-07-16

arxiv.org/abs/hep-th/9407097v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages; LaTeX; IFUM 461/FT

Scientific paper

We discuss the relations between (topological) quantum field theories in 4 dimensions and the theory of 2-knots (embedded 2-spheres in a 4-manifold). The so-called BF theories allow the construction of quantum operators whose trace can be considered as the higher-dimensional generalization of Wilson lines for knots in 3-dimensions. First-order perturbative calculations lead to higher dimensional linking numbers, and it is possible to establish a heuristic relation between BF theories and Alexander invariants. Functional integration-by-parts techniques allow the recovery of an infinitesimal version of the Zamolodchikov tetrahedron equation, in the form considered by Carter and Saito.

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