Projective resolutions of coherent sheaves and descent relations between branes

Details Projective resolutions of coherent sheaves and descent relations between branes Projective resolutions of coherent sheaves and descent relations between branes

1999-08-02

arxiv.org/abs/hep-th/9908009v2

Adv.Theor.Math.Phys. 4 (2002) 617-626

Physics

High Energy Physics

High Energy Physics - Theory

1+8 pages, no figures; v2: enhanced language

Scientific paper

We notice that, for branes wrapped on complex analytic subvarieties, the algebraic-geometric version of K-theory makes the identification between brane-antibrane pairs and lower-dimensional branes automatic. This is because coherent sheaves on the ambient variety represent gauge bundles on subvarieties, and they can be put in exact sequences (projective resolutions) with sheaves corresponding to vector bundles on the pair; this automatically gives a D(p-2) as a formal difference of bundles on the Dp - D\bar p pair, both belonging to the Grothendieck group of coherent sheaves of the ambient.

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