Two-dimensional abelian BF theory in Lorenz gauge as a twisted N=(2,2) superconformal field theory

TL;DR

This paper reveals that the two-dimensional abelian BF theory in Lorenz gauge can be viewed as a twisted N=(2,2) superconformal field theory, establishing a surprising connection between topological gauge theories and superconformal models.

Contribution

It demonstrates that the gauge-fixed abelian BF theory is equivalent to a free type B twisted N=(2,2) superconformal theory, enabling new avenues for deformations.

Findings

The gauge-fixed theory is a free type B twisted N=(2,2) superconformal theory.

The ghost field corresponds to the pullback of a holomorphic coordinate.

The BRST operator matches the total Q of the twisted theory.

Abstract

We study the two-dimensional topological abelian BF theory in the Lorenz gauge and, surprisingly, we find that the gauged-fixed theory is a free type B twisted N=(2,2) superconformal theory with odd linear target space, with the ghost field c being the pullback of the linear holomorphic coordinate on the target. The BRST operator of the gauge-fixed theory equals the total Q of type B twisted theory. This unexpected identification of two different theories opens a way for nontrivial deformations of both of these theories.