Investigación

 

Remarks on noncommutative solitons

 

H. García-Compeán* and J. Moreno**

 

Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000, México D.F., México. e-mail: *compean@fis.cinvestav.mx, **jmoreno@fis.cinvestav.mx

 

Recibido el 11 de abril de 2002.
Aceptado el 18 de septiembre de 2002.

 

Abstract

In the first part of this work we consider an unstable non-BPS Dp — p—brane pair in Type II superstring theory. Turning on a background NS-NS B—field (constant and nonzero along two spatial directions), we show that the tachyon responsible for the unstability has a complex GMS solitonic solution, which is interpreted as the low energy remnant of the resulting D(p — 2)—brane. In the second part, we apply these results to construct the noncommutative soliton analogous of Witten's superconducting string. This is done by considering the complex GMS soliton arising from the D3 — 3—brane annihilation in Type IIB superstring theory. In the presence of left-handed fermions, we apply the Weyl-Wigner-Moyal correspondence and the bosonization technique to show that this object behaves like a superconducting wire.

Keywords: Non-BPS branes, noncommutative soliton, superconducting string.

 

Resumen

En la primera parte de este trabajo consideramos un par inestable de D-branas no-BPS, Dp — p, en la teoría de supercuerdas tipo II. Considerando un campo de fondo B NS-NS (constante y diferente de cero a lo largo de dos direcciones espaciales), mostramos que el taquión responsable de la inestabilidad corresponde a una solución solitónica compleja del tipo GMS, la cual puede ser interpretada como el remanente de bajas energías de la D(p— 2) resultante. En la segunda parte, aplicamos estos resultados para construir un solitón noconmutativo análogo a la cuerda superconductora de Witten. Esto se hace considerando un solitón complejo GMS que proviene de la aniquilación de un par D3 — 3 en la teoría de supercuerdas tipo IIB. En la presencia de fermiones izquierdos, aplicamos la correspondencia de Weyl-Wigner-Moyal y la técnica de bosonización para mostrar que este objeto se comporta como un alambre superconductor.

Descriptores: Branas no-BPS, solitones noconmutativos, cuerdas superconductoras.

 

PACS: 11.10.-z; 11.25.-w; 11.27.+d

 

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Acknowledgments

We are greatful to A. Güijosa, O. Loaiza-Brito and M. Przanowski, for useful discussions. We thank R. Tatar for pointing out Ref. 27. This work was supported in part by the CONACYT grants No. 33951E and 30420E.

 

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