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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.N. Atmaja and H.S. Ramadhan, Bogomol’nyi equations of classical solutions, Phys. Rev. D 90 (2014) 105009 [arXiv:1406.6180] [INSPIRE].
D. Bazeia, E. da Hora, C. dos Santos and R. Menezes, BPS Solutions to a Generalized Maxwell-Higgs Model, Eur. Phys. J. C 71 (2011) 1833 [arXiv:1201.2974] [INSPIRE].
E.B. Bogomolny, Stability of Classical Solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [INSPIRE].
E. Babichev, Global topological k-defects, Phys. Rev. D 74 (2006) 085004 [hep-th/0608071] [INSPIRE].
E. Babichev, Gauge k-vortices, Phys. Rev. D 77 (2008) 065021 [arXiv:0711.0376] [INSPIRE].
S. Sarangi, DBI global strings, JHEP 07 (2008) 018 [arXiv:0710.0421] [INSPIRE].
E. Babichev, P. Brax, C. Caprini, J. Martin and D.A. Steer, Dirac Born Infeld (DBI) Cosmic Strings, JHEP 03 (2009) 091 [arXiv:0809.2013] [INSPIRE].
O.V. Pavlovsky, Chiral Born-Infeld theory: Topological spherically symmetrical solitons, Phys. Lett. B 538 (2002) 202 [hep-ph/0204313] [INSPIRE].
H.S. Ramadhan, Higher-dimensional DBI Solitons, Phys. Rev. D 85 (2012) 065014 [arXiv:1201.1591] [INSPIRE].
H.S. Ramadhan, On DBI Textures with Generalized Hopf Fibration, Phys. Lett. B 713 (2012) 297 [arXiv:1205.6282] [INSPIRE].
R. Casana, M.M. Ferreira Jr., E. da Hora and C. dos Santos, Analytical BPS Maxwell-Higgs vortices, Adv. High Energy Phys. 2014 (2014) 210929 [arXiv:1405.7920] [INSPIRE].
R. Casana, M.M. Ferreira Jr. and E. da Hora, Generalized BPS magnetic monopoles, Phys. Rev. D 86 (2012) 085034 [arXiv:1210.3382] [INSPIRE].
R. Casana, M.M. Ferreira Jr., E. da Hora and C. dos Santos, Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario, Phys. Lett. B 722 (2013) 193 [arXiv:1304.3382] [INSPIRE].
D. Bazeia, R. Casana, M.M. Ferreira Jr., E. da Hora and L. Losano, Deformed self-dual magnetic monopoles, Phys. Lett. B 727 (2013) 548 [arXiv:1311.4817] [INSPIRE].
M.K. Prasad and C.M. Sommerfield, An Exact Classical Solution for the ’t Hooft Monopole and the Julia-Zee Dyon, Phys. Rev. Lett. 35 (1975) 760 [INSPIRE].
G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].
N.S. Manton and P. Sutcliffe, Topological solitons, Cambridge University Press, Cambridge, U.K. (2004), pg. 493.
D. Bazeia, R. Casana, M.M. Ferreira Jr. and E. da Hora, Nontopological self-dual Maxwell-Higgs vortices, Europhys. Lett. 109 (2015) 21001 [arXiv:1502.05063] [INSPIRE].
S. Lipschutz and M.R. Spiegel, Schaum’s Outlines of Mathematical Handbook of Formulas and tables, 3rd edition, The McGraw-Hill Companies Inc. (2009).
C. Adam, C. Naya, J. Sanchez-Guillen, J.M. Speight and A. Wereszczynski, Thermodynamics of the BPS Skyrme model, Phys. Rev. D 90 (2014) 045003 [arXiv:1405.2927] [INSPIRE].
C. Adam, C. Naya, J. Sanchez-Guillen, R. Vazquez and A. Wereszczynski, Neutron stars in the Bogomol’nyi-Prasad-Sommerfield Skyrme model: Mean-field limit versus full field theory, Phys. Rev. C 92 (2015) 025802 [arXiv:1503.03095] [INSPIRE].
C. Adam, T. Klähn, C. Naya, J. Sanchez-Guillen, R. Vazquez and A. Wereszczynski, Baryon chemical potential and in-medium properties of BPS skyrmions, Phys. Rev. D 91 (2015) 125037 [arXiv:1504.05185] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1505.01241
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)117