Families of gauge conditions in BV formalism

Abstract

In BV formalism we can consider a Lagrangian submanifold as a gauge condition. Starting with the BV action functional we construct a closed form on the space of Lagrangian submanifolds. If the action functional is invariant with respect to some group H and Lambda is an H-invariant family of Lagrangian submanifold then under certain conditions we construct a form on Lambda that descends to a closed form on Lambda/H. Integrating the latter form over a cycle in Lambda/H we obtain numbers that can have interesting physical meaning. We show that one can get string amplitudes this way. Applying this construction to topological quantum field theories one obtains topological invariants.