Towards construction of geometric bosonic quantum field theories I

We present a geometric construction of 2D chiral boson theories on manifolds with tangent bundle admitting flat connection with possible torsion. The construction is based on embedding of the theory into the supersymmetric $\beta\gamma-bc$ system. To perform the embedding we do a covariant smooth point-splitting of vector field observables and then the fermions are killed by a strongly oscillating chiral gauge transformation.