D-Branes, Derived Categories, and Grothendieck Groups
High Energy Physics - Theory
2008-11-26 v1
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 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.
Keywords
Cite
@article{arxiv.hep-th/9902116,
title = {D-Branes, Derived Categories, and Grothendieck Groups},
author = {Eric R. Sharpe},
journal= {arXiv preprint arXiv:hep-th/9902116},
year = {2008}
}
Comments
LaTeX, 21 pages