Deformation of graded Poisson (Batalin-Vilkovisky) structures

A Batalin-Vilkovisky formalism is a most general framework to construct consistent quantum field theories. Its mathematical structure is called a Batalin-Vilkovisky structure. First we explain the mathematical setting of a Batalin-Vilkovisky formalism. Next, we consider deformation theory of a Batalin-Vilkovisky structure. Especially, we consider deformation of topological sigma models in any dimension, which is closely related to many deformation theories in mathematics, including deformation from commutative geometry to noncommutative geometry. We obtain a series of new nontrivial topological sigma models and we find these models have the Batalin-Vilkovisky structures based on a series of new algebroids.