Abstract
p-Balls are topological defects in (D, 1) dimensions constructed with \( \mathrm{\mathcal{M}}\ge 1 \) scalar fields which depend radially on only 2 ≤ p ≤ D − 2 spatial dimensions. Such defects are characterized by an action that breaks translational invariance and are inspired on the physics of a brane with D − p extra dimensions. Here we consider the issue of localization of bosonic states described by a scalar field Φ sufficiently weak to not disturb sensibly the defect configuration. After describing the general formalism, we consider some specify examples with \( \mathrm{\mathcal{M}} \) = 1, 2 and 3, looking for some region of parameters where bound and resonant bosonic states can be found. We investigate the way the influence of the defect structure, number of radial dimensions and coupling between the fields are related to the occurrence of bound and resonant states.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Vilenkin, Cosmic strings and other topological defects, Cambridge University Press, Cambridge (1994).
N. Manton and P. Sutcliffe, Topological Solitons, Cambridge University Press, Cambridge (2004).
J. Greensite, The Confinement problem in lattice gauge theory, Prog. Part. Nucl. Phys. 51 (2003) 1 [hep-lat/0301023] [INSPIRE].
T. Suzuki, Monopoles and confinement, Nucl. Phys. Proc. Suppl. 30 (1993) 176 [INSPIRE].
M.N. Chernodub and M.I. Polikarpov, Abelian Projections and Monopoles, in Confinement, Duality, and Nonperturbative Aspects of QCD, NATO Science Series: B: volume 368. Advanced Science Institutes Series, P. van Baal ed., Springer US (2002), p. 387 [hep-th/9710205] [INSPIRE].
M.N. Chernodub and V.I. Zakharov, Magnetic component of Yang-Mills plasma, Phys. Rev. Lett. 98 (2007) 082002 [hep-ph/0611228] [INSPIRE].
M.N. Chernodub, K. Ishiguro, A. Nakamura, T. Sekido, T. Suzuki and V.I. Zakharov, Topological defects and equation of state of gluon plasma, PoS(LATTICE 2007)174 [arXiv:0710.2547] [INSPIRE].
M.N. Chernodub, A. Nakamura and V.I. Zakharov, Manifestations of magnetic vortices in equation of state of Yang-Mills plasma, Phys. Rev. D 78 (2008) 074021 [arXiv:0807.5012] [INSPIRE].
A. Anabalon, S. Willison and J. Zanelli, The Universe as a topological defect, Phys. Rev. D 77 (2008) 044019 [hep-th/0702192] [INSPIRE].
P. Mukherjee, J. Urrestilla, M. Kunz, A.R. Liddle, N. Bevis and M. Hindmarsh, Detecting and distinguishing topological defects in future data from the CMBPol satellite, Phys. Rev. D 83 (2011) 043003 [arXiv:1010.5662] [INSPIRE].
M. Sakellariadou, Production of Topological Defects at the End of Inflation, Lect. Notes Phys. 738 (2008) 359 [hep-th/0702003] [INSPIRE].
P.P. Avelino, C.J.A.P. Martins, C. Santos and E.P.S. Shellard, Topological defects in contracting universes, Phys. Rev. Lett. 89 (2002) 271301 [Erratum ibid. 89 (2002) 289903] [astro-ph/0211066] [INSPIRE].
P.P. Avelino and L. Sousa, Domain wall network evolution in (N + 1)-dimensional FRW universes, Phys. Rev. D 83 (2011) 043530 [arXiv:1101.3360] [INSPIRE].
J.C.Y. Teo and C.L. Kane, Topological Defects and Gapless Modes in Insulators and Superconductors, Phys. Rev. B 82 (2010) 115120 [arXiv:1006.0690] [INSPIRE].
M.A. Silaev and G.E. Volovik, Topological superfluid 3 He-B: fermion zero modes on interfaces and in the vortex core, J. Low Temp. Phys. 161 (2010) 460 [arXiv:1005.4672].
T. Fukui and T. Fujiwara, Z 2 index theorem for Majorana zero modes in a class D topological superconductor, Phys. Rev. B 82 (2010) 184536 [arXiv:1009.2582] [INSPIRE].
T.Sh. Misirpashaev and G.E. Volovik, Fermion zero modes in symmetric vortices in superfluid 3 He, Physica B 210 (1995) 338.
G.E. Volovik, Flat band in the core of topological defects: Bulk-vortex correspondence in topological superfluids with Fermi points, JETP Lett. 93 (2011) 66 [Pisma Zh. Eksp. Teor. Fiz. 93 (2011) 69] [arXiv:1011.4665] [INSPIRE].
H.B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].
G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
A.M. Polyakov, Particle Spectrum in the Quantum Field Theory, JETP Lett. 20 (1974) 194 [Pisma Zh. Eksp. Teor. Fiz. 20 (1974) 430] [INSPIRE].
V.A. Rubakov and M.E. Shaposhnikov, Do We Live Inside a Domain Wall?, Phys. Lett. B 125 (1983) 136 [INSPIRE].
V.A. Rubakov and M.E. Shaposhnikov, Extra Space-Time Dimensions: Towards a Solution to the Cosmological Constant Problem, Phys. Lett. B 125 (1983) 139 [INSPIRE].
E.J. Squires, Dimensional Reduction Caused by a Cosmological Constant, Phys. Lett. B 167 (1986) 286 [INSPIRE].
M. Visser, An Exotic Class of Kaluza-Klein Models, Phys. Lett. B 159 (1985) 22 [hep-th/9910093] [INSPIRE].
K. Akama, An Early Proposal of ‘Brane World’, Lect. Notes Phys. 176 (1982) 267 [hep-th/0001113] [INSPIRE].
I. Antoniadis, A Possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [INSPIRE].
D. Finkelstein, Kinks, J. Math. Phys. 7 (1966) 1218 [INSPIRE].
O. DeWolfe, D.Z. Freedman, S.S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [INSPIRE].
M. Gremm, Four-dimensional gravity on a thick domain wall, Phys. Lett. B 478 (2000) 434 [hep-th/9912060] [INSPIRE].
M. Gremm, Thick domain walls and singular spaces, Phys. Rev. D 62 (2000) 044017 [hep-th/0002040] [INSPIRE].
A. Kehagias and K. Tamvakis, A selftuning solution of the cosmological constant problem, Mod. Phys. Lett. A 17 (2002) 1767 [hep-th/0011006] [INSPIRE].
C. Csáki, J. Erlich, T.J. Hollowood and Y. Shirman, Universal aspects of gravity localized on thick branes, Nucl. Phys. B 581 (2000) 309 [hep-th/0001033] [INSPIRE].
A. Campos, Critical phenomena of thick branes in warped space-times, Phys. Rev. Lett. 88 (2002) 141602 [hep-th/0111207] [INSPIRE].
R. Guerrero, A. Melfo and N. Pantoja, Selfgravitating domain walls and the thin wall limit, Phys. Rev. D 65 (2002) 125010 [gr-qc/0202011] [INSPIRE].
D. Bazeia, C. Furtado and A.R. Gomes, Brane structure from scalar field in warped space-time, JCAP 02 (2004) 002 [hep-th/0308034] [INSPIRE].
D. Bazeia and A.R. Gomes, Bloch brane, JHEP 05 (2004) 012 [hep-th/0403141] [INSPIRE].
D. Bazeia, F.A. Brito and A.R. Gomes, Locally localized gravity and geometric transitions, JHEP 11 (2004) 070 [hep-th/0411088] [INSPIRE].
V. Dzhunushaliev, V. Folomeev and M. Minamitsuji, Thick brane solutions, Rept. Prog. Phys. 73 (2010) 066901 [arXiv:0904.1775] [INSPIRE].
A.G. Cohen and D.B. Kaplan, Solving the hierarchy problem with noncompact extra dimensions, Phys. Lett. B 470 (1999) 52 [hep-th/9910132] [INSPIRE].
R. Gregory, Nonsingular global string compactifications, Phys. Rev. Lett. 84 (2000) 2564 [hep-th/9911015] [INSPIRE].
T. Gherghetta and M.E. Shaposhnikov, Localizing gravity on a stringlike defect in six dimensions, Phys. Rev. Lett. 85 (2000) 240 [hep-th/0004014] [INSPIRE].
M. Giovannini, H. Meyer and M.E. Shaposhnikov, Warped compactification on Abelian vortex in six-dimensions, Nucl. Phys. B 619 (2001) 615 [hep-th/0104118] [INSPIRE].
P. Peter, C. Ringeval and J.-P. Uzan, Stability of six-dimensional hyperstring brane worlds, Phys. Rev. D 71 (2005) 104018 [hep-th/0301172] [INSPIRE].
O. Corradini and Z. Kakushadze, A solitonic 3-brane in 6D bulk, Phys. Lett. B 506 (2001) 167 [hep-th/0103031] [INSPIRE].
Y. Kodama, K. Kokubu and N. Sawado, Localization of massive fermions on the baby-skyrmion branes in 6 dimensions, Phys. Rev. D 79 (2009) 065024 [arXiv:0812.2638] [INSPIRE].
Y. Brihaye, T. Delsate, N. Sawado and Y. Kodama, Inflating baby-Skyrme branes in six dimensions, Phys. Rev. D 82 (2010) 106002 [arXiv:1007.0736] [INSPIRE].
O. Corradini, A. Iglesias, Z. Kakushadze and P. Langfelder, Gravity on a 3-brane in 6D bulk, Phys. Lett. B 521 (2001) 96 [hep-th/0108055] [INSPIRE].
M. Giovannini, Gravitating multidefects from higher dimensions, Phys. Rev. D 75 (2007) 064023 [hep-th/0612104] [INSPIRE].
Z. Horvath and L. Palla, Spontaneous Compactification and ‘Monopoles’ in Higher Dimensions, Nucl. Phys. B 142 (1978) 327 [INSPIRE].
G.W. Gibbons and P.K. Townsend, Self-gravitating Yang Monopoles in all Dimensions, Class. Quant. Grav. 23 (2006) 4873 [hep-th/0604024] [INSPIRE].
E.B. Bogomolny, Stability of Classical Solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [Yad. Fiz. 24 (1976) 861] [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].
D. Bazeia, J. Menezes and R. Menezes, New global defect structures, Phys. Rev. Lett. 91 (2003) 241601 [hep-th/0305234] [INSPIRE].
D. Bazeia, J. Menezes and R. Menezes, Global defects in field theory with applications to condensed matter, Mod. Phys. Lett. B 19 (2005) 801 [cond-mat/0511657] [INSPIRE].
R. Casana, A.R. Gomes, R. Menezes and F.C. Simas, Trapping of Spin-0 fields on tube-like topological defects, Phys. Lett. B 730 (2014) 8 [arXiv:1309.4360] [INSPIRE].
R. Casana, A.R. Gomes, G.V. Martins and F.C. Simas, Trapping Dirac fermions in tubes generated by two scalar fields, Phys. Rev. D 89 (2014) 085036 [arXiv:1307.7579] [INSPIRE].
C. Ringeval, P. Peter and J.-P. Uzan, Localization of massive fermions on the brane, Phys. Rev. D 65 (2002) 044016 [hep-th/0109194] [INSPIRE].
R. Davies and D.P. George, Fermions, scalars and Randall-Sundrum gravity on domain-wall branes, Phys. Rev. D 76 (2007) 104010 [arXiv:0705.1391] [INSPIRE].
Y.-X. Liu, C.-E. Fu, L. Zhao and Y.-S. Duan, Localization and Mass Spectra of Fermions on Symmetric and Asymmetric Thick Branes, Phys. Rev. D 80 (2009) 065020 [arXiv:0907.0910] [INSPIRE].
S.L. Dubovsky, V.A. Rubakov and P.G. Tinyakov, Brane world: Disappearing massive matter, Phys. Rev. D 62 (2000) 105011 [hep-th/0006046] [INSPIRE].
C.A.S. Almeida, M.M. Ferreira Jr., A.R. Gomes and R. Casana, Fermion localization and resonances on two-field thick branes, Phys. Rev. D 79 (2009) 125022 [arXiv:0901.3543] [INSPIRE].
Y.-X. Liu, J. Yang, Z.-H. Zhao, C.-E. Fu and Y.-S. Duan, Fermion Localization and Resonances on A de Sitter Thick Brane, Phys. Rev. D 80 (2009) 065019 [arXiv:0904.1785] [INSPIRE].
Y.-X. Liu, H.-T. Li, Z.-H. Zhao, J.-X. Li and J.-R. Ren, Fermion Resonances on Multi-field Thick Branes, JHEP 10 (2009) 091 [arXiv:0909.2312] [INSPIRE].
Y.-X. Liu, C.-E. Fu, H. Guo, S.-W. Wei and Z.-H. Zhao, Bulk Matters on a GRS-Inspired Braneworld, JCAP 12 (2010) 031 [arXiv:1002.2130] [INSPIRE].
W.T. Cruz, A.R. Gomes and C.A.S. Almeida, Fermions on deformed thick branes, Eur. Phys. J. C 71 (2011) 1790 [arXiv:1110.4651] [INSPIRE].
B. Bajc and G. Gabadadze, Localization of matter and cosmological constant on a brane in anti-de Sitter space, Phys. Lett. B 474 (2000) 282 [hep-th/9912232] [INSPIRE].
H. Guo, A. Herrera-Aguilar, Y.-X. Liu, D. Malagon-Morejon and R.R. Mora-Luna, Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb’s law on a pure de Sitter thick braneworld, Phys. Rev. D 87 (2013) 095011 [arXiv:1103.2430] [INSPIRE].
H. Guo, Y.-X. Liu, Z.-H. Zhao and F.-W. Chen, Thick branes with a non-minimally coupled bulk-scalar field, Phys. Rev. D 85 (2012) 124033 [arXiv:1106.5216] [INSPIRE].
R.H. Hobart, On the Instability of a Class of Unitary Field Models, Proc. Phys. Soc. 82 (1963) 201.
G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].
R. Rajaraman, Solitons and Instantons, North-Holland, Amsterdan (1982).
D. Bazeia and F.A. Brito, Tiling the plane without supersymmetry, Phys. Rev. Lett. 84 (2000) 1094 [hep-th/9908090] [INSPIRE].
D. Bazeia, H. Boschi-Filho and F.A. Brito, Domain defects in systems of two real scalar fields, JHEP 04 (1999) 028 [hep-th/9811084] [INSPIRE].
A. de Souza Dutra, M.B. Hott and C.A.S. Almeida, Remarks on supersymmetry of quantum systems with position dependent effective masses, Europhys. Lett. 62 (2003) 8 [hep-th/0306078] [INSPIRE].
E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].
B. Wang, C.-Y. Lin and C. Molina, Quasinormal behavior of massless scalar field perturbation in Reissner-Nordstrom anti-de Sitter spacetimes, Phys. Rev. D 70 (2004) 064025 [hep-th/0407024] [INSPIRE].
S. Hashi, A. Sandovici, H.S.V. de Snoo and H. Winkler, Form Sums of Nonnegative Selfadjoint Operators, Acta Math. Hung. 111 (2006) 81.
C.R. Frye and C.J. Efthimiou, Spherical Harmonics in p Dimensions, arXiv:1205.3548 [INSPIRE].
J.S. Avery, Harmonic polynomials, hyperspherical harmonics, and atomic spectra, J. Comput. Appl. Math. 233 (2010) 1366.
J.S. Avery, Hypershperical Hermonics: Applications in Quantum Theory, Kluwer Academic Publishers, Dordrecht (1989).
D. Bazeia, M.J. dos Santos and R.F. Ribeiro, Solitons in systems of coupled scalar fields, Phys. Lett. A 208 (1995) 84 [hep-th/0311265] [INSPIRE].
D. Bazeia, L. Losano and C. Wotzasek, Domain walls in three field models, Phys. Rev. D 66 (2002) 105025 [hep-th/0206031] [INSPIRE].
A. Alonso Izquierdo, M.A. González León and J. Mateos Guilarte, Stability of Kink Defects in a Deformed O(3) Linear Sigma Model, Nonlinearity 15 (2002) 1097 [math-ph/0204041].
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: 1502.02912v1
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., Gomes, A.R. & Simas, F.C. Trapping Spin-0 particles on p-balls in (D, 1) dimensions. J. High Energ. Phys. 2015, 135 (2015). https://doi.org/10.1007/JHEP06(2015)135
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2015)135