BV Quantization of Topological Open Membranes

TL;DR

This paper explores the deformation of boundary string theories in topological open membranes with a WZ coupling, revealing how a 3-form field induces a trilinear bracket that deforms the boundary algebra structure.

Contribution

It introduces a perturbative approach to analyze bulk-boundary correlators and demonstrates how a 3-form field deforms the boundary homotopy Lie algebra structure.

Findings

The 3-form C-field induces a trilinear bracket in the boundary algebra.

Perturbative expansion reveals deformation of the homotopy Lie algebra.

First step towards quantizing quasi-Lie bialgebroids.

Abstract

We study bulk-boundary correlators in topological open membranes. The basic example is the open membrane with a WZ coupling to a 3-form. We view the bulk interaction as a deformation of the boundary string theory. This boundary string has the structure of a homotopy Lie algebra, which can be viewed as a closed string field theory. We calculate the leading order perturbative expansion of this structure. For the 3-form field we find that the C-field induces a trilinear bracket, deforming the Lie algebra structure. This paper is the first step towards a formal universal quantization of general quasi-Lie bialgebroids.