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A study of the Higgs and confining phases in Euclidean SU(2) Yang–Mills theories in 3d by taking into account the Gribov horizon

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Abstract

We study SU(2) three-dimensional Yang–Mills theories in presence of Higgs fields in the light of the Gribov phenomenon. By restricting the domain of integration in the functional integral to the first Gribov horizon, we are able to discuss a kind of transition between the Higgs and the confining phase in a semiclassical approximation. Both adjoint and fundamental representation for the Higgs field are considered, leading to a different phase structure.

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Notes

  1. See [11, 12] for a pedagogical introduction to the Gribov problem.

  2. These configurations are instantons in Euclidean space-time.

  3. We recall here that the terms logβ and logω can be neglected in the derivation of the gap equations, Eqs. (33), (34), when taking the thermodynamic limit, see [10–12] for details.

  4. The Higgs mass ν 2 is then the only mass scale entering the game.

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Acknowledgements

The Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq-Brazil), the Faperj, Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, the Latin American Center for Physics (CLAF), the SR2-UERJ, the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) are gratefully acknowledged. D.D. is supported by the Research-Foundation Flanders.

Sorella’s work is supported by FAPERJ, Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/101.578/2010.

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Authors and Affiliations

  1. Departamento de Física Teórica, Instituto de Física, UERJ—Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Rio de Janeiro, 20550-013, Maracanã, Brazil

    M. A. L. Capri, A. J. Gómez, M. S. Guimaraes, I. F. Justo & S. P. Sorella

  2. Department of Physics and Astronomy, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium

    D. Dudal

Authors
  1. M. A. L. Capri
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  2. D. Dudal
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  3. A. J. Gómez
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  4. M. S. Guimaraes
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  5. I. F. Justo
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  6. S. P. Sorella
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Correspondence to M. S. Guimaraes.

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Capri, M.A.L., Dudal, D., Gómez, A.J. et al. A study of the Higgs and confining phases in Euclidean SU(2) Yang–Mills theories in 3d by taking into account the Gribov horizon. Eur. Phys. J. C 73, 2346 (2013). https://doi.org/10.1140/epjc/s10052-013-2346-5

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  • DOI: https://doi.org/10.1140/epjc/s10052-013-2346-5

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