D-branes, open string vertex operators, and Ext groups
arXiv:hep-th/0208104 · doi:10.4310/ATMP.2002.v6.n6.a1
Abstract
In this paper we explicitly work out the precise relationship between Ext groups and massless modes of D-branes wrapped on complex submanifolds of Calabi-Yau manifolds. Specifically, we explicitly compute the boundary vertex operators for massless Ramond sector states, in open string B models describing Calabi-Yau manifolds at large radius, directly in BCFT using standard methods. Naively these vertex operators are in one-to-one correspondence with certain sheaf cohomology groups (as is typical for such vertex operator calculations), which are related to the desired Ext groups via spectral sequences. However, a subtlety in the physics of the open string B model has the effect of physically realizing those spectral sequences in BRST cohomology, so that the vertex operators are actually in one-to-one correspondence with Ext group elements. This gives an extremely concrete physical test of recent proposals regarding the relationship between derived categories and D-branes. We check these results extensively in numerous examples, and comment on several related issues.
48 pages, 1 figure, LaTeX; v2: material on Freed-Witten added; v3: ATMP submission, obsoleted by v2; v4 = v2
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