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

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

2010-11-30

arxiv.org/abs/1012.0026v1

Phys.Lett.B697:488-492,2011

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 8 figures

Scientific paper

10.1016/j.physletb.2011.02.030

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.

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