D-branes, orbifolds, and Ext groups

Details D-branes, orbifolds, and Ext groups D-branes, orbifolds, and Ext groups

2002-12-18

arxiv.org/abs/hep-th/0212218v3

Nucl.Phys. B673 (2003) 263-300

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, 3 figures; v2: material on Freed-Witten added; v3: more typos fixed

Scientific paper

10.1016/j.nuclphysb.2003.09.022

In this note we extend previous work on massless Ramond spectra of open strings connecting D-branes wrapped on complex manifolds, to consider D-branes wrapped on smooth complex orbifolds. Using standard methods, we calculate the massless boundary Ramond sector spectra directly in BCFT, and find that the states in the spectrum are counted by Ext groups on quotient stacks (which provide a notion of homological algebra relevant for orbifolds). Subtleties that cropped up in our previous work also appear here. We also use the McKay correspondence to relate Ext groups on quotient stacks to Ext groups on (large radius) resolutions of the quotients. As stacks are not commonly used in the physics community, we include pedagogical discussions of some basic relevant properties of stacks.

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