Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-02-16
Nucl.Phys.B561:433-450,1999
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 21 pages
Scientific paper
10.1016/S0550-3213(99)00535-0
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 worldvolume, in addition to information about the smooth 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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