Abstract
We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a k-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of F μν F μν. We have implemented our proposal by means of a k-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol’nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of k-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with |ϕ|4-potential or |ϕ|6-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the k-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Manton and P. Sutcliffe, Topological solitons, Cambridge University Press, Cambridge U.K. (2004).
D. Bazeia, E. da Hora, C. dos Santos and R. Menezes, Generalized self-dual Chern-Simons vortices, Phys. Rev. D 81 (2010) 125014 [arXiv:1006.3955] [INSPIRE].
D. Bazeia, E. da Hora, R. Menezes, H.P. de Oliveira and C. dos Santos, Compact-like kinks and vortices in generalized models, Phys. Rev. D 81 (2010) 125016 [arXiv:1004.3710] [INSPIRE].
C. dos Santos and E. da Hora, Domain walls in a generalized Chern-Simons model, Eur. Phys. J. C 70 (2010) 1145 [INSPIRE].
C. dos Santos and E. da Hora, Lump-like solitons in a generalized Abelian-Higgs Chern-Simons model, Eur. Phys. J. C 71 (2011) 1519 [INSPIRE].
C. dos Santos, Compact solitons in an abelian-Higgs Chern-Simons model, Phys. Rev. D 82 (2010) 125009 [INSPIRE].
D. Bazeia, E. da Hora and D. Rubiera-Garcia, Compact vortex in a generalized Born-Infeld model, Phys. Rev. D 84 (2011) 125005 [arXiv:1103.4940] [INSPIRE].
C. dos Santos and D. Rubiera-Garcia, Generalized sine-Gordon solitons, J. Phys. A 44 (2011) 425402 [arXiv:1106.4060] [INSPIRE].
D. Bazeia, R. Casana, E. da Hora and R. Menezes, Generalized self-dual Maxwell-Chern-Simons-Higgs model, Phys. Rev. D 85 (2012) 125028 [arXiv:1206.0998] [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, 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].
C. Adam, L.A. Ferreira, E. da Hora, A. Wereszczynski and W.J. Zakrzewski, Some aspects of self-duality and generalised BPS theories, JHEP 08 (2013) 062 [arXiv:1305.7239] [INSPIRE].
R. Casana et al., Analytical BPS Maxwell-Higgs Vortices, Adv. High Energy Phys. 2014 (2014) 210929.
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. 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].
C. Adam, N. Grandi, J. Sanchez-Guillen and A. Wereszczynski, K fields, compactons and thick branes, J. Phys. A 41 (2008) 212004 [Erratum ibid. A 42 (2009) 159801] [arXiv:0711.3550] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, k-defects as compactons, J. Phys. A 40 (2007) 13625 [Erratum ibid. A 42 (2009) 089801] [arXiv:0705.3554] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A BPS Skyrme model and baryons at large-N c , Phys. Rev. D 82 (2010) 085015 [arXiv:1007.1567] [INSPIRE].
C. Adam, N. Grandi, P. Klimas, J. Sanchez-Guillen and A. Wereszczynski, Compact self-gravitating solutions of quartic K-fields in brane cosmology, J. Phys. A 41 (2008) 375401 [arXiv:0805.3278] [INSPIRE].
C. Adam, P. Klimas, J. Sanchez-Guillen and A. Wereszczynski, Compact gauge K vortices, J. Phys. A 42 (2009) 135401 [arXiv:0811.4503] [INSPIRE].
M. Andrews, M. Lewandowski, M. Trodden and D. Wesley, Distinguishing k-defects from their canonical twins, Phys. Rev. D 82 (2010) 105006 [arXiv:1007.3438] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, N = 1 supersymmetric extension of the baby Skyrme model, Phys. Rev. D 84 (2011) 025008 [arXiv:1105.1168] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Supersymmetric K field theories and defect structures, Phys. Rev. D 84 (2011) 065032 [arXiv:1107.4370] [INSPIRE].
P.P. Avelino, D. Bazeia and R. Menezes, Localized D-dimensional global k-defects, Eur. Phys. J. C 71 (2011) 1683 [arXiv:1007.1457] [INSPIRE].
D. Bazeia, J.D. Dantas, A.R. Gomes, L. Losano and R. Menezes, Twinlike models in scalar field theories, Phys. Rev. D 84 (2011) 045010 [arXiv:1105.5111] [INSPIRE].
A. Mostafazadeh, Imaginary-scaling versus indefinite-metric quantization of the Pais-Uhlenbeck oscillator, Phys. Rev. D 84 (2011) 105018 [arXiv:1107.1874] [INSPIRE].
C. Adam and J.M. Queiruga, An algebraic construction of twin-like models, Phys. Rev. D 84 (2011) 105028 [arXiv:1109.4159] [INSPIRE].
C. Adam and J.M. Queiruga, Twinlike models with identical linear fluctuation spectra, Phys. Rev. D 85 (2012) 025019 [arXiv:1112.0328] [INSPIRE].
C. Adam, C. Naya, J. Sanchez-Guillen and A. Wereszczynski, The vector BPS Skyrme model, Phys. Rev. D 86 (2012) 085001 [arXiv:1208.2465] [INSPIRE].
C. Adam, C. Naya, J. Sanchez-Guillen and A. Wereszczynski, The vector BPS baby Skyrme model, Phys. Rev. D 86 (2012) 045015 [arXiv:1207.0517] [INSPIRE].
D. Bazeia, E. da Hora and R. Menezes, Twinlike models for self-dual abelian-Higgs theories, Phys. Rev. D 85 (2012) 045005 [arXiv:1111.6542] [INSPIRE].
D. Bazeia, A.S. Lobao, Jr. and R. Menezes, Twinlike models for kinks and compactons in flat and warped spacetime, Phys. Rev. D 86 (2012) 125021 [arXiv:1210.6874] [INSPIRE].
D. Bazeia and R. Menezes, New results on twinlike models, Phys. Rev. D 84 (2011) 125018 [arXiv:1111.1318] [INSPIRE].
C. Armendariz-Picon, T. Damour and V.F. Mukhanov, k-inflation, Phys. Lett. B 458 (1999) 209 [hep-th/9904075] [INSPIRE].
V. Mukhanov and A. Vikman, Searching for a holographic connection between dark energy and the low l CMB multipoles, JCAP 02 (2005) 004.
C. Armendariz-Picon and E.A. Lim, Haloes of k-essence, JCAP 08 (2005) 007.
J. Garriga and V.F. Mukhanov, Perturbations in k-inflation, Phys. Lett. B 458 (1999) 219 [hep-th/9904176] [INSPIRE].
R.J. Scherrer, Purely kinetic k-essence as unified dark matter, Phys. Rev. Lett. 93 (2004) 011301 [astro-ph/0402316] [INSPIRE].
M. Giovannini, Gauge field localization on Abelian vortices in six-dimensions, Phys. Rev. D 66 (2002) 044016 [hep-th/0205139] [INSPIRE].
K. Shiraishi and S. Hirenzaki, Bogomolny equations for vortices in Born-Infeld-Higgs systems, Int. J. Mod. Phys. A 6 (1991) 2635 [INSPIRE].
R. Casana, E. da Hora, D. Rubiera-Garcia and C. dos Santos, Topological vortices in generalized Born-Infeld-Higgs electrodynamics, Eur. Phys. J. C 75 (2015) 380 [arXiv:1507.08793] [INSPIRE].
A. Vilenkin, Cosmic strings and domain walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. 91B (1980) 99 [INSPIRE].
S.M. Carroll, V. Duvvuri, M. Trodden and M.S. Turner, Is cosmic speed - up due to new gravitational physics?, Phys. Rev. D 70 (2004) 043528 [astro-ph/0306438] [INSPIRE].
K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
A. De Felice, D.F. Mota and S. Tsujikawa, Matter instabilities in general Gauss-Bonnet gravity, Phys. Rev. D 81 (2010) 023532 [arXiv:0911.1811] [INSPIRE].
M. Sakellariadou, Cosmic strings and cosmic superstrings, Nucl. Phys. Proc. Suppl. 192-193 (2009) 68 [arXiv:0902.0569] [INSPIRE].
E.B. Bogomolny, Stability of classical solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [INSPIRE].
H.J. de Vega and F.A. Schaposnik, A classical vortex solution of the abelian Higgs model, Phys. Rev. D 14 (1976) 1100 [INSPIRE].
J. Hong, Y. Kim and P.Y. Pac, On the multivortex solutions of the abelian Chern-Simons-Higgs theory, Phys. Rev. Lett. 64 (1990) 2230 [INSPIRE].
R. Jackiw and E.J. Weinberg, Selfdual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990) 2234 [INSPIRE].
R. Jackiw, K. Lee and E.J. Weinberg, Selfdual Chern-Simons solitons, Phys. Rev. D 42 (1990) 3488 [INSPIRE].
H.B. Nielsen and P. Olesen, Vortex line models for dual strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].
E. Babaev, Vortices carrying an arbitrary fraction of magnetic flux quantum in two gap superconductors, Phys. Rev. Lett. 89 (2002) 067001 [cond-mat/0111192] [INSPIRE].
E. Babev, J. Jäykkä and M. Speight, Magnetic field delocalization and flux inversion in fractional vortices in two-component superconductors, Phys. Rev. Lett. 103 (2009) 237002.
M.M. Anber, Y. Burnier, E. Sabancilar and M. Shaposhnikov, Diamagnetic vortices in Chern Simons theory, Phys. Rev. D 92 (2015) 085049 [arXiv:1508.05284] [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: 1509.04654
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
Casana, R., Cavalcante, A. & da Hora, E. Self-dual configurations in Abelian Higgs models with k-generalized gauge field dynamics. J. High Energ. Phys. 2016, 51 (2016). https://doi.org/10.1007/JHEP12(2016)051
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2016)051