String field theory and brane superpotentials

TL;DR

This paper develops a string field theory framework for D-brane superpotentials, providing an intrinsic, all-orders computation method and clarifying their relation to Chern-Simons actions.

Contribution

It introduces a homotopy Maurer-Cartan approach to describe D-brane superpotentials within topological string field theory, unifying moduli space descriptions.

Findings

Derived an A-infty algebra structure for tree-level string products.

Established an equivalence between moduli space descriptions via Maurer-Cartan and homotopy Maurer-Cartan.

Provided a method to compute D-brane superpotentials to all orders.

Abstract

I discuss tree-level amplitudes in cubic topological string field theory, showing that a certain family of gauge conditions leads to an A-infty algebra of tree-level string products which define a potential describing the dynamics of physical states. Upon using results of modern deformation theory, I show that the string moduli space admits two equivalent descriptions, one given in standard Maurer-Cartan fashion and another given in terms of a `homotopy Maurer-Cartan problem', which describes the critical set of the potential. By applying this construction to the topological A and B models, I obtain an intrinsic formulation of `D-brane superpotentials' in terms of string field theory data. This gives a prescription for computing such quantities to all orders, and proves the equivalence of this formulation with the fundamental description in terms of string field moduli. In particular, it clarifies the relation between the Chern-Simons/holomorphic Chern-Simons actions and the superpotential for A/B-type branes.