Journal of High Energy Physics

, 2016:117 | Cite as

More on Bogomol’nyi equations of three-dimensional generalized Maxwell-Higgs model using on-shell method

  • A. N. AtmajaEmail author
  • H. S. Ramadhan
  • E. da Hora
Open Access
Regular Article - Theoretical Physics


We use a recent on-shell method, developed in [1], to construct Bogomol’nyi equations of the three-dimensional generalized Maxwell-Higgs model [2]. The resulting Bogomol’nyi equations are parametrized by a constant C 0 and they can be classified into two types determined by the value of C 0 = 0 and C 0 ≠ 0. We identify that the Bogomol’nyi equations obtained by Bazeia et al. [2] are of the (C 0 = 0)-type Bogomol’nyi equations. We show that the Bogomol’nyi equations of this type do not admit the Prasad-Sommerfield limit in its spectrum. As a resolution, the vacuum energy must be lifted up by adding some constant to the potential. Some possible solutions whose energy equal to the vacuum are discussed briefly. The on-shell method also reveals a new (C 0 ≠ 0)-type Bogomol’nyi equations. This non-zero C 0 is related to a non-trivial function \( {f}_{{\mathrm{C}}_0} \) defined as a difference between energy density of the scalar potential term and of the gauge kinetic term. It turns out that these Bogomol’nyi equations correspond to vortices with locally non-zero pressures, while their average pressure \( \mathcal{P} \) remain zero globally by the finite energy constraint.


Solitons Monopoles and Instantons Field Theories in Lower Dimensions 


Open Access

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Quantum Science Centre, Department of Physics, Faculty of ScienceUniversity of MalayaKuala LumpurMalaysia
  2. 2.Research Center for Physics, Indonesian Institute of Sciences (LIPI)TangerangIndonesia
  3. 3.Departemen Fisika, FMIPAUniversitas IndonesiaDepokIndonesia
  4. 4.Coordenadoria Interdisciplinar de Ciência e Tecnologia & Departemento de FísicaUniversidade Federal do MaranhãoSão LuísBrazil

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