Abelian BF Theories and Knot Invariants

Abstract

In the context of the Batalin-Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander-Conway polynomial. The three-dimensional case is analyzed explicitly, and it is proved to be anomaly free. Moreover, at the second order in perturbation theory, a new formula for the second coefficient of the Alexander-Conway polynomial is obtained. An account on the higher-dimensional generalizations is also given.

50 pages, LaTeX file; a few minor corrections added

References in corpus (1)

• Cabled Wilson Loops in BF Theories

Cited by in corpus (4)

• The Hitchin functionals and the topological B-model at one loop
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
• Abelian BF theory and Turaev-Viro invariant
• BRST Symmetries for the Tangent Gauge Group