Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branes as Stable Holomorphic Line Bundles On the Non-Commutative Torus   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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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn