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arXiv · hep-th/0403126

Branes as Stable Holomorphic Line Bundles On the Non-Commutative Torus

Pascal Grange
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Abstract

It was recently suggested by A. Kapustin that turning on a $B$-field, and allowing some discrepancy between the left and and right-moving complex structures, must induce an identification of B-branes with holomorphic line bundles on a non-commutative complex torus. We translate the stability condition for the branes into this language and identify the stable topological branes with previously proposed non-commutative instanton equations. This involves certain topological identities whose derivation has become familiar in non-commutative field theory. It is crucial for these identities that the instantons are localized. We therefore explore the case of non-constant field strength, whose non-linearities are dealt with thanks to the rank-one Seiberg--Witten map.

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Pascal Grange. 2004-03-11. Branes as Stable Holomorphic Line Bundles On the Non-Commutative Torus. https://doi.org/10.1088/1126-6708%2F2004%2F10%2F002

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