Holomorphic potentials for graded D-branes

TL;DR

This paper develops a holomorphic potential framework for graded D-branes in Calabi-Yau spaces, connecting string field theory with homotopy algebra and analyzing moduli spaces and condensates.

Contribution

It introduces a generalized holomorphic potential for graded D-branes, linking string field theory and homotopy algebra, and explores their moduli spaces and condensate formations.

Findings

Holomorphic potential generalizes known superpotentials.

Moduli space descriptions align with homotopy algebra results.

Graded D-brane pairs can form acyclic condensates and two-form condensates.

Abstract

We discuss gauge-fixing, propagators and effective potentials for topological A-brane composites in Calabi-Yau compactifications. This allows for the construction of a holomorphic potential describing the low-energy dynamics of such systems, which generalizes the superpotentials known from the ungraded case. Upon using results of homotopy algebra, we show that the string field and low energy descriptions of the moduli space agree, and that the deformations of such backgrounds are described by a certain extended version of `off-shell Massey products' associated with flat graded superbundles. As examples, we consider a class of graded D-brane pairs of unit relative grade. Upon computing the holomorphic potential, we study their moduli space of composites. In particular, we give a general proof that such pairs can form acyclic condensates, and, for a particular case, show that another branch of their moduli space describes condensation of a two-form.