D-branes, open string vertex operators, and Ext groups

Sheldon Katz, Eric Sharpe

Research output: Contribution to journalArticlepeer-review


In this note 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. The Freed-Witten anomaly also plays an important role in these calculations, and we are now able to completely reconcile that anomaly with the derived categories program generally. We check these results extensively in numerous examples, and comment on several related issues.

Original languageEnglish (US)
Pages (from-to)979-1030
Number of pages52
JournalAdvances in Theoretical and Mathematical Physics
Issue number6
StatePublished - Nov 2002

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


Dive into the research topics of 'D-branes, open string vertex operators, and Ext groups'. Together they form a unique fingerprint.

Cite this