Quantum gauge fields and flat connections in 2-dimensional BF theory

TL;DR

This paper demonstrates that the flat connection governing correlation functions in 2D BF theory arises from the quantum equations of motion, linking gauge theory, topological models, and quantum algebraic structures.

Contribution

It establishes that the flatness of the Torossian connection in 2D BF theory follows from the properly regularized quantum equations of motion.

Findings

Flatness of the Torossian connection is derived from quantum equations of motion.

The connection is related to the KZ connection in the WZW model.

The work links gauge theory, topological models, and quantum algebra.

Abstract

The 2-dimensional BF theory is both a gauge theory and a topological Poisson $\sigma$-model corresponding to a linear Poisson bracket. In \cite{To1}, Torossian discovered a connection which governs correlation functions of the BF theory with sources for the $B$-field. This connection is flat, and it is a close relative of the KZ connection in the WZW model. In this paper, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.