O. Obregón
Instituto de Física de la Universidad de Guanajuato, P.O. Box E–143, 37150 León Gto., México, e–mail: octavio@fisica.ugto.mx
Recibido el 1 de mayo de 2006
Aceptado el 1 de noviembre de 2006
Abstract
]]> We propose a non–Abelian Born–Infeld theory based on an Abelian theory by Erwin Schrodinger that, as he showed, is equivalent to Born–Infeld theory. Its construction does not require at any stage the square root structure that characterizes the Dirac–Born–Infeld (DBI) action. Various non–Abelian generalizations are possible. We focus our attention, in this work, in one of them. For it, it is shown that Instantons solutions exist.Our formalism could be of interest in connection with string theory and possible extensions of well known physical results in the usual Born–Infeld Abelian case.Keywords: Born–Infeld; Non–Abelian.
Resumen
Se propone una teoría no–Abeliana de Born–Infeld basada en una teoría Abeliana de Erwin Schrodinger que, como él lo ha mostrado, es equivalente a la teoría propuesta por Born e Infeld. Su construcción no requiere en ninguna etapa de la estructura de raíz cuadrada que caracteriza la acción Dirac–Born–Infeld (DBI). Varias generalizaciones no Abelianas son posibles; nos centramos en este trabajo en una de ellas. Para esto, se muestra que las soluciones de Instantones existen. Nuestro formalismo puede ser de interés en conexión con teoría de cuerdas y posibles extensiones de resultados físicos bien conocidos en el caso de Born–Infeld Abeliano usual.
Descriptores: Born–Infeld; no–Abeliano.
PACS: 11.15.–q; 11.90.+t
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]]>Acknowledgments
I would like to thank H. García–Compéan, G. W. Gibbons, J. López, C. Ramírez and M. Sabido for helpful comments and suggestions on this manuscript. This work was supported in part by CONACyT grant 47641, Universidad de Guanajuato and PROMEP grants.
References
1. E. Schrödinger, Proc. Roy. Soc. A 150 (1935) 465. [ Links ]
2. M. Born, Nature 132 (1933) 282. [ Links ]
3. M. Born, Proc. Roy. Soc. A 143 (1934) 410. [ Links ]
4. M. Born and L. Infeld, Nature 132 (1933) 970. [ Links ]
5. M. Born and L. Infeld, PROC. ROY. SOC. A 144 (1934) 425. [ Links ]
6. M. Born and L. Infeld, Proc. Roy. Soc. A 147 (1934) 522. [ Links ]
7. J.H. Schwarz, Comments on Born–Infeld Theory, ArXiv:hep–th/0103165. [ Links ]
8. P.C. Argyres and C.R. Nappi, Nucl. Phys. B 330 (1990) 151. [ Links ]
9. A.A. Tseytlin, Nucl. Phys. B 501 (1997) 42. [ Links ]
10. A. Hashimoto and W.I. Taylor, Nucl. Phys. B 503 (1997) 193. [ Links ]
11. E.A. Bergshoeff, A. Bilal, M. de Roo and A. Sevrin, JHEP 0107 (2001) 029. [ Links ]
12. As is well known, in the usual Born–Infeld theory the square root can be avoided by introducing an auxiliary field. Its equation of motion, when substituted in the modified action gives once more the square root structure. See M. Rocek and A.A. Tseytlin, Phys. Rev. D 59 (1999) 106001. The proposal here is, however, completely different. [ Links ]
13. G.A. Goldin and V.M. Shtelen, J. Phys. A 37 (2004) 10711. [ Links ]
14. in Eq. (27) hermitian conjugation could also have been cosidered. [ Links ]
15. Probably one of these two possibilities could be more appropiate to search them in connection with string theory, because it is argued that the open string effective Lagrangian should have (at tree level) a single trace (or symmetrized trace) over the group indices. See by example C.V. Johnson, D–Branes (Cambridge University Press, 2003). [ Links ]
16. A.A. Belavin, A.M. Polyakov, A.S. Schwartz, and Yu S. Tyupkin, Phys. Lett. B 59 (1975) 85. [ Links ]
17. See by example S. Weinberg, The Quantum Theory of Fields, Vol. 2: Modern Applications (Cambridge University Press, 1996). [ Links ]
18. See by example, G.W. Gibbons, Nucl. Phys. B 454 (1995) 185. [ Links ] ]]>