Abstract
This paper considers the Einstein equations coupled with the nonabelian gauge and Higgs fields. It is shown that, when cosmic string solutions are sought in the Einstein-Georgi-Glashow system and the Einstein-Weinberg-Salam system governing the gravitational-electromagnetic-weak interaction forces, the self duality conditions lead to positive values of the cosmological constant which can be expressed by some fundamental parameters in particle physics.
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[AO1] Ambjorn, J., Olesen, P.: Anti-screening of large magnetic fields by vector bosons. Phys. Lett.B214, 565–569 (1988)
[AO2] Ambjorn, J., Olesen, P.: A magnetic condensate solution of the classical electroweak theory. Phys. Lett.B218, 67–71 (1989)
[AO3] Ambjorn, J., Olesen, P.: On electroweak magnetism. Nucl. Phys.B315, 606–614 (1989)
[A] Aubin, T.: Nonlinear Analysis on Manifolds: Monge-Ampére Equations. Berlin, Heidelberg, New York: Springer, 1989
[BLP] Berestycki, H., Lions, P.L., Peletier, L. A.: An ODE approach to the existence of positive solutions for semilinear problems ℝN. Indiana Univ. Math. J.30, 141–157 (1981)
[CG] Comtet, A., Gibbons, G. W.: Bogomol'nyi bounds for cosmic strings. Nucl. Phys.B299, 719–733 (1988)
[CHMcY] Chen, X., Hastings, S., McLeod, J. B., Yang, Y.: A nonlinear elliptic equation arising from gauge field theory and cosmology. Proc. R. Soc. London. Series A, to appear
[JT] Jaffe, A., Taubes, C.: Vortices and Monopoles, Boston: Birkhäuser, 1980
[KW] Kazdan, J. L., Warner, F. W.: Curvature functions for open 2-manifolds. Ann. of Math.99, 203–219 (1974)
[L1] Linet, B.: A vortex-line model for a system of cosmic strings in equilibrium. Gen. Relat. Grav.20, 451–456 (1988)
[L2] Linet, B.: On the supermassiveU(1) gauge cosmic strings, Class. Quantum Grav.7, L75-L79 (1990)
[SWYMc] Smoller, J., Wasserman, A., Yau, S.-T., McLeod, J.B.: Smooth static solutions of the Einstein/Yang-Mills equations. Bull. Am. Math. Soc.27, 239–242 (1992)
[SY1] Spruck, J., Yang, Y.: On multivortices in the electroweak theory II: Existence of Bogomol'nyi solutions in ℝ2. Commun. Math. Phys.144, 215–234 (1992)
[SY2] Spruck, J., Yang, Y.: Cosmic string solutions of the Einstein-matter-gauge equations. Preprint, 1992
[V] Vilenkin, A.: Cosmic strings and domain walls. Phys. Rep.121, 263–315 (1985)
[W] Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys.61, 1–23 (1989)
[Y] Yang, Y.: Existence of massiveSO(3) vortices. J. Math. Phys.32, 1395–1399 (1991)
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Communicated by R. H. Dijkgraaf
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Yang, Y. Self duality of the gauge field equations and the cosmological constant. Commun.Math. Phys. 162, 481–498 (1994). https://doi.org/10.1007/BF02101744
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DOI: https://doi.org/10.1007/BF02101744