Two-dimensional abelian BF theory in Lorenz gauge as a twisted N=(2,2) superconformal field theory
arXiv:1712.01186 · doi:10.1016/j.geomphys.2018.05.009
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.
Ver. 2: a discussion of the relation of descent to AKSZ construction added. Ver. 3: section 2.5.2 (a toy example of Gromov-Witten invariant) corrected; section 2.5.1 expanded with comments on the BV generating function for the action of a vector field