Derived brackets in bosonic string sigma-model

Abstract

We study the worldsheet theory of bosonic string from the point of view of the BV formalism. We explicitly describe the derived Poisson structure which arises when we expand the Master Action near a Lagrangian submanifold. The resulting higher Poisson brackets are all degenerate and essentially constant along their symplectic leaves. Deformations of the worldsheet complex structures define a family of Lagrangian submanifolds, parametrized by Beltrami differential. The worldsheet action depends nonlinearly on the Beltrami differential, but the structure of nonlinearity is governed by the BV Master Equation. This helps to clarify the mechanism of holomorphic factorization of string amplitudes.