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Multiple condensate solutions for the Chern-Simons-Higgs theory. (English) Zbl 0863.58081
Summary: We study the existence of condensate solutions for the Chern-Simons-Higgs model with the choice of a potential field where both the symmetric and asymmetric vacua occur as ground states [see J. Hong, Y. Kim and P. Y. Pac, Phys. Rev. Lett. 64, No. 19, 2230-2233 (1990) and R. Jackiw and E. J. Weinberg, ibid., 2234-2237 (1990)]. We show that if the Chern-Simons coupling parameter \(k\) is above a critical value, no such solutions can exist, while for \(k>0\) below this critical value there exist at least two condensate solutions carrying the same quantized energy, as well as electric and magnetic charge. This multiplicity result accounts for the two vacua states present in the model. In fact, as \(k\to 0^+\) it is shown that the two solutions found “bifurcate” from the asymmetric and symmetric vacuum states, respectively.

MSC:
58Z05 Applications of global analysis to the sciences
81T13 Yang-Mills and other gauge theories in quantum field theory
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