BRANE SUPERPOTENTIAL AND LOCAL CALABI–YAU MANIFOLDS
Abstract
We briefly report on some recent progresses in the computation of B-brane superpotentials for Type II strings compactified on Calabi–Yau manifolds, obtained by using a paramatrization 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 for the cases in which there exists a holomorphic projection from the local space around the curve to the curve itself.
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