Generalized holomorphic bundles and the B-field action

TL;DR

This paper explores generalized holomorphic bundles on complex manifolds, focusing on the B-field action's effects and connections to Nahm's equations and holomorphic gerbes, revealing new insights into their structure and transformations.

Contribution

It introduces the B-field action on generalized holomorphic bundles and analyzes its impact, linking it to co-Higgs bundles, Nahm's equations, and holomorphic gerbes.

Findings

B-field action modifies generalized holomorphic bundles

Connections established with Nahm's equations

Relations to holomorphic gerbes elucidated

Abstract

On a generalized complex manifold there is an associated definition of a generalized holomorphic bundle, introduced by Gualtieri. This notion in the case of an ordinary complex structure yields an object which we call a co-Higgs bundle and we consider the B-field action of a closed form of type (1,1), both local and global. The effect makes contact with both Nahm's equations and holomorphic gerbes.