# Mathematical aspects of D-branes

@article{Sharpe2004MathematicalAO, title={Mathematical aspects of D-branes}, author={Eric Sharpe}, journal={arXiv: High Energy Physics - Theory}, year={2004}, pages={614-620} }

In these notes we review recent work on describing D-branes with nonzero Higgs vevs in terms of sheaves, which gives a physical on-shell D-brane interpretation to more sheaves than previously understood as describing D-branes. The mathematical ansatz for this encoding is checked by comparing open string spectra between D-branes with nonzero Higgs vevs to Ext groups between the corresponding sheaves. We illustrate the general methods with a few examples.

## 4 Citations

### B-branes and the derived category

- Mathematics
- 2004

By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted…

### 2-block Springer fibers: convolution algebras and coherent sheaves

- Mathematics
- 2008

For a fixed 2-block Springer fiber, we describe the structure of its irreducible components and their relation to the Bialynicki-Birula paving, following work of Fung. That is, we consider the space…

### Convolution Algebras, Coherent Sheaves, and Embedded Tqft

- Mathematics

For a fixed 2-block Springer fiber, we describe the structure of its irreducible components and their relation to the Białynicki-Birula paving, following work of Fung. We define a convolution algebra…

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By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted…

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