On Globalized Traces for the Poisson Sigma Model

A globalized version of a trace formula for the Poisson Sigma Model on the disk is presented by using its formal global picture in the setting of the Batalin–Vilkovisky formalism. This global construction includes the concept of zero modes. Moreover, for the symplectic case of the Poisson Sigma Model with cotangent target, the globalized trace reduces to a symplectic construction which was presented by Grady, Li and Li for 1-dimensional Chern–Simons theory (topological quantum mechanics). In addition, the connection between this formula and the Nest–Tsygan theorem and the Tamarkin–Tsygan theorem is explained.