Abstract
The 2-dimensional BF theory is both a gauge theory and a topological Poisson σ-model corresponding to a linear Poisson bracket. In [3], 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 Letter, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.
Highlights
The 2-dimensional BF theory is both a gauge theory and a topological Poisson σ-model corresponding to a linear Poisson bracket
In [3], 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
We show that flatness of the Torossian connection follows from quantum equations of motion of the BF theory
Summary
The 2-dimensional BF theory is a an interesting example of a model which is at the same time a gauge theory and a (topological) Poisson σ-model corresponding to a linear Poisson bracket. The Kontsevich approach to quantization is to fix the gauge and to study the Feynman graphs of the model [2] In this context, Torossian [3] discovered a very interesting flat connection which governs the behavior of correlation functions of exponentials of the B-field. Our aim in this paper is to better understand the origin of the Torossian connection from the point of view of gauge theory To this end, we consider the BF theory with source terms for the B-field placed at the points z1, .
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
