Isaac Scientific Publishing

# Journal of Advances in Applied Mathematics

### Cohomological Vertex Operators

Download PDF (829.8 KB) PP. 71 - 88 Pub. Date: March 23, 2017

### Author(s)

• ANDRÉS VIÑA*
Departamento de Física, Universidad de Oviedo, Avda Calvo Sotelo, 33007 Oviedo, Spain

### 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 pairs. We also interpret some strings with ghost number k as obstructions for lifts or extensions of strings with ghost number k − 1.

### Keywords

B-branes, vertex operators, derived categories of sheaves

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