BF Theories and 2-knots
High Energy Physics - Theory
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.hep-th/9407097,
title = {BF Theories and 2-knots},
author = {P. Cotta-Ramusino and M. Martellini},
journal= {arXiv preprint arXiv:hep-th/9407097},
year = {2007}
}
Comments
16 pages; LaTeX; IFUM 461/FT