Brane superpotential and local Calabi-Yau manifolds

TL;DR

This paper discusses recent advances in calculating B-brane superpotentials for Type II string compactifications on Calabi-Yau manifolds, providing a closed-form expression for certain local space configurations.

Contribution

It introduces a new closed-form expression for B-brane superpotentials on genus-g curves within Calabi-Yau threefolds under specific projection conditions.

Findings

Derived a closed expression for superpotentials

Applicable to local spaces with holomorphic projections

Advances understanding of brane dynamics in Calabi-Yau geometries

Abstract

We briefly report on some recent progress in the computation of B-brane superpotentials for Type II strings compactified on Calabi-Yau manifolds, obtained by using a parametrization of tubular neighborhoods of complex submanifolds, also known as local spaces. In particular, we propose a closed expression for the superpotential of a brane on a genus-g curve in a Calabi-Yau threefold in the case in which there exists a holomorphic projection from the local space around the curve to the curve itself.