# 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…

### 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…

### 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…

## References

SHOWING 1-10 OF 21 REFERENCES

### D-branes, categories and N=1 supersymmetry

- Mathematics
- 2000

We show that boundary conditions in topological open string theory on Calabi–Yau (CY) manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry…

### D-Branes And K-Theory

- Philosophy
- 1998

By exploiting recent arguments about stable nonsupersymmetric D-brane states, we argue that D-brane charge takes values in the K-theory of spacetime, as has been suspected before. In the process, we…

### Anomalies in string theory with D-branes

- Mathematics
- 1999

We analyze global anomalies for elementary Type II strings in the presence of D-branes. Global anomaly cancellation gives a restriction on the D-brane topology. This restriction makes possible the…

### Spectra of D-branes with Higgs vevs

- Mathematics
- 2003

In this paper we continue previous work on counting open string states between D-branes by considering open strings between D-branes with nonzero Higgs vevs, and in particular, nilpotent Higgs vevs,…

### D-branes, B fields, and Ext groups

- Mathematics
- 2003

In this paper we extend previous work on calculating massless boundary Ramond sector spectra of open strings to include cases with nonzero flat B fields. In such cases, D-branes are no longer…

### Derived Categories and Zero-Brane Stability

- Mathematics
- 2001

We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This…

### 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…