Cohomological vertex operators

Abstract

Given a Calabi-Yau manifold and considering the $B$-branes on it as objects in the derived category of coherent sheaves, we identify the vertex operators for strings between two branes with elements of the cohomology groups of Ext sheaves. We define the correlation functions for these general vertex operators. Strings stretching between two coherent sheaves are studied as homological extensions of the corresponding branes. In this context, we relate strings between different pairs of branes when there are maps between these branes. We also interpret some strings with ghost number $k$ as obstructions for lifts or extensions of strings with ghost number $k-1$.

Version which will appear in Journal of Advances in Applied Mathematics

References in corpus (2)

• D-branes, open string vertex operators, and Ext groups
• D-branes and $K$-homology

Cited by in corpus (1)

• Spanning Class in the Category of Branes