Topological BF Theories in 3 and 4 Dimensions
Aberto S. Cattaneo, Paolo Cotta-Ramusino, Juerg Froehlich, Maurizio, Martellini
TL;DR
This paper explores topological BF theories in 3 and 4 dimensions, focusing on their associated knot invariants like Alexander and HOMFLY polynomials, and their role in topological quantum field theory.
Contribution
It provides an analysis of observables in BF theories related to knots and links, highlighting their connection to known topological invariants in 3 and 4 dimensions.
Findings
Invariants include Alexander and HOMFLY polynomials
Vacuum expectation values yield topological invariants
Main focus on 3-dimensional case with knot invariants
Abstract
In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide range of invariants. Here we consider mainly the 3-dimensional case, where these invariants include Alexander polynomials, HOMFLY polynomials and Kontsevich integrals.
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