Math @ Duke
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Publications [#9517] of Eric Sharpe
Papers Published
- Eric Sharpe, D-Branes, Derived Categories, and Grothendieck Groups,
Nucl. Phys. B561 (1999) 433-450
[hep-th/9902116]
(last updated on 1999/12/20)
Abstract: In this paper we describe how Grothendieck groups of
coherent sheaves and locally free sheaves can be used to
describe type II D-branes, in the case that all D-branes are
wrapped on complex varieties and all connections are
holomorphic. Our proposal is in the same spirit as recent
discussions of K-theory and D-branes; within the restricted
class mentioned, Grothendieck groups encode a choice of
connection on each D-brane world-volume, in addition to
information about the C^\infty bundles. We also point out
that derived categories can also be used to give insight
into D-brane constructions, and analyze how a Z_2 subset of
the T-duality group acting on D-branes on tori can be
understood in terms of a Fourier-Mukai transformation.
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