H. García–Compeán*, O. Obregón** and C. Ramírez***
* Departamento de Física Centro de Investigación y de Estudios Avanzados del IPN P.O. Box 14–740, 07000, Mexico D.F., México
** Instituto de Física de la Universidad de Guanajuato, P.O. Box E–143, 37150, León Gto., México
*** Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla, P.O. Box 1364, 72000, Puebla, México
Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005
Abstract
Noncommutative gravity is a very interesting subject that has not yet been successfully related to string theory. However, it can be motivated by itself by the consideration of a description of the microscopic structure of spacetime, leaving for the future its precise connection to string theory or M–theory. In this paper we review some of the recent attempts to make sense of the noncommutative description of some classical theories of gravity by using the Seiberg–Witten map. In particular we describe noncommutative topological gravity and a gauge invariant proposal generalizing Plebanski–Ashtekar Self–dual gravity.
Keywords: Noncommutative field theory; Seiberg–Witten map; topological gravity; self–dual gravity.
Resumen
La gravedad no conmutativa es un tema muy interesante que, hasta ahora, no ha sido incluido en la teoría de cuerdas. Sin embargo, este tema puede ser motivado mediante la consideración de una descripción microscópica de la estructura del espacio–tiempo, dejando para el futuro su relación precisa con la teoría de cuerdas o la teoría M. En este artículo, revisamos algunos de los intentos recientes para dar sentido a la descripción noconmutativa de algunas teorías clásicas de la gravedad, mediante el uso del mapeo de Seiberg–Witten. En particular, describimos la gravedad topológica no conmutativa y una propuesta no conmutativa e invariante de norma que generaliza la gravedad auto–dual de Plebanski–Ashtekar.
Descriptores: Teoría de campos no conmutativa; mapeo de Seiberg–Witten; gravedad topológica; gravedad auto–dual.
PACS: 11.10.Nx; 04.20.Cv; 04.20.Gz; 11.15.Kc
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Acknowledgments
This work was supported in part by CONACyT México Grant Nos. 37851E, 33951E and 41993E.
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