Abstract
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.
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ArXiv ePrint: 1505.01241
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Atmaja, A.N., Ramadhan, H.S. & da Hora, E. More on Bogomol’nyi equations of three-dimensional generalized Maxwell-Higgs model using on-shell method. J. High Energ. Phys. 2016, 117 (2016). https://doi.org/10.1007/JHEP02(2016)117
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DOI: https://doi.org/10.1007/JHEP02(2016)117