We present the BFV and the BV extension of the Poisson sigma model (PSM) 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, in contrast to those theories, 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, which are new also for the ordinary PSM and promise adaptations to other Lie algebroid-based gauge theories: The BV functional, in particular, is the sum of the classical action, the Hamiltonian lift of the (only on-shell nilpotent) BRST differential, and a term quadratic in the antifields which is essentially the basic curvature and measures the compatibility of \(\nabla \) with the Lie algebroid structure on \(T^*M\). We finally construct a \(\hbox {Diff}(M)\)-equivariant isomorphism between the two BV formulations.

我们提出了由封闭的3形式H扭曲的Poisson sigma模型（PSM）的BFV和BV扩展。这些功能存在超域版本，例如用于PSM，更一般而言，用于AKSZ sigma模型。但是，与那些理论相反，它们取决于源流形的欧拉矢量场，并且包含将源流和目标流形的数据混合在一起的项。在目标歧管M上使用辅助连接\（\ nabla \），我们获得了不使用超场的替代的纯几何表达式，这对于普通的PSM也是新的，并有望适应其他基于李代数的规范理论：BV函数，特别是经典动作的总和，哈密​​顿量（仅壳上幂零）的BRST微分和反场中的一个二次项，其本质上是基本曲率，并测量\（\ nabla \）与\（T ^ * M上的李代数结构的相容性\）。最后，我们在两个BV公式之间构造了一个\（\ hbox {Diff}（M）\）等价同构。