Batalin–Vilkovisky formalism beyond perturbation theory via derived geometry

Abstract: In this talk I will discuss applications of derived differential geometry to study a non-perturbative generalisation of classical Batalin–Vilkovisky (BV-)formalism. First, I will describe the current state of the art of the geometry of perturbative BV-theory. Then, I will introduce a simple model of derived differential geometry, whose geometric objects are formal derived smooth stacks (i.e. stacks on formal derived smooth manifolds), and which is obtained by applying Töen-Vezzosi’s homotopical algebraic geometry to the theory of derived manifolds of Spivak and Carchedi-Steffens. I will show how derived differential geometry is able to capture aspects of non-perturbative BV-theory by means of examples in the cases of scalar field theory and Yang-Mills theory.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)