My talk is based on the paper 'BV and BFV for the H-twisted Poisson sigma model' with Thomas Strobl, e-Print: 1912.13511 [hep-th].
We present the BFV and the BV extension of the Poisson sigma model twisted by a closed 3-form $H$. There exist superfield versions of these functionals such as for the PSM and, more generally, for the AKSZ sigma models. However, they depend on the Euler vector field of the source manifold and contain terms mixing data from the source and the target manifold.
Using an auxiliary connection $\nabla$ on the target manifold $M$, we obtain alternative, purely geometrical expressions without the use of superfields.