SIGMA 9 (2013), 067, 7 pages      arXiv:1309.0650      https://doi.org/10.3842/SIGMA.2013.067
Contribution to the Special Issue on Deformations of Space-Time and its Symmetries

An Index for Intersecting Branes in Matrix Models

Harold Steinacker and Jochen Zahn
Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria

Received September 17, 2013; Published online November 08, 2013

Abstract
We introduce an index indicating the occurrence of chiral fermions at the intersection of branes in matrix models. This allows to discuss the stability of chiral fermions under perturbations of the branes.

Key words: matrix models; noncommutative geometry; chiral fermions.

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References

1. Aoki H., Chiral fermions and the standard model from the matrix model compactified on a torus, Progr. Theoret. Phys. 125 (2011), 521-536, arXiv:1011.1015.
2. Berenstein D., Dzienkowski E., Matrix embeddings on flat R³ and the geometry of membranes, Phys. Rev. D 86 (2012), 086001, 19 pages, arXiv:1204.2788.
3. Berkooz M., Douglas M.R., Leigh R.G., Branes intersecting at angles, Nuclear Phys. B 480 (1996), 265-278, hep-th/9606139.
4. Berline N., Getzler E., Vergne M., Heat kernels and Dirac operators, Grundlehren der Mathematischen Wissenschaften, Vol. 298, Springer-Verlag, Berlin, 1992.
5. Blumenhagen R., Cvetic M., Langacker P., Shiu G., Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55 (2005), 71-139, hep-th/0502005.
6. Chatzistavrakidis A., Steinacker H., Zoupanos G., Intersecting branes and a standard model realization in matrix models, J. High Energy Phys. 2011 (2011), no. 9, 115, 36 pages, arXiv:1107.0265.
7. Gauntlett J.P., Intersecting branes, hep-th/9705011.
8. Ishibashi N., Kawai H., Kitazawa Y., Tsuchiya A., A large-N reduced model as superstring, Nuclear Phys. B 498 (1997), 467-491, hep-th/9612115.
9. Kato T., Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Vol. 132, Springer-Verlag, New York, 1966.
10. Nishimura J., Tsuchiya A., Realizing chiral fermions in the type IIB matrix model at finite N, arXiv:1305.5547.
11. Steinacker H., Emergent gravity from noncommutative gauge theory, J. High Energy Phys. 2007 (2007), no. 12, 049, 36 pages, arXiv:0708.2426.
12. Steinacker H., Emergent geometry and gravity from matrix models: an introduction, Classical Quantum Gravity 27 (2010), 133001, 46 pages, arXiv:1003.4134.
13. Steinacker H., Split noncommutativity and compactified brane solutions in matrix models, Progr. Theoret. Phys. 126 (2011), 613-636, arXiv:1106.6153.