Abelian BF Theories and Knot Invariants

TL;DR

This paper introduces a new observable in Abelian BF theory within the Batalin-Vilkovisky formalism, linking it to the Alexander-Conway polynomial and deriving new formulas for its coefficients.

Contribution

It proposes a novel observable in Abelian BF theory, establishes its relation to knot invariants, and provides explicit calculations and generalizations.

Findings

Vacuum expectation value related to Alexander-Conway polynomial

Anomaly-free analysis in three dimensions

New formula for the second coefficient of the polynomial

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.