TL;DR
This paper derives a general geometric framework for supersymmetry conditions and BPS bounds for D-branes in type II backgrounds, extending calibration concepts to more complex, dynamic configurations with electric flux.
Contribution
It introduces a comprehensive geometric approach to supersymmetry conditions for D-branes, including non-static and electric flux configurations, expanding previous partial results.
Findings
Derived supersymmetry conditions and BPS bounds for D-branes
Extended calibration concepts to general supersymmetric configurations
Applied framework to fundamental strings as an example
Abstract
A geometrical form of the supersymmetry conditions for D-branes on arbitrary type II supersymmetric backgrounds is derived, as well as the associated BPS bounds. The treatment is general and allows to consider, for instance, non-static configurations or D-branes supporting a non-vanishing electric flux, hence completing previous partial results. In particular, our discussion clarifies how the notion of calibration can be extended in order to be applicable to the most general supersymmetric configurations. As an exemplifying preliminary step, the procedure followed is first applied to fundamental strings.
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