Abstract
We explore a variety of composite topological structures that arise from the spontaneous breaking of SO(10) to SU(3)c × U(1)em via one of its maximal subgroups SU(5) × U(1)χ, SU(4)c × SU(2)L × SU(2)R, and SU(5) × U(1)X (also known as flipped SU(5)). They include i) a network of ℤ strings which develop monopoles and turn into necklaces with the structure of ℤ2 strings, ii) dumbbells connecting two different types of monopoles, or monopoles and antimonpoles, iii) starfish-like configurations, iv) polypole configurations, and v) walls bounded by a necklace. We display these structures both before and after the electroweak breaking. The appearance of these composite structures in the early universe and their astrophysical implications including gravitational wave emission would depend on the symmetry breaking patterns and scales, and the nature of the associated phase transitions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D 10 (1974) 275 [INSPIRE].
H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].
H. Georgi, The State of the Art—Gauge Theories, AIP Conf. Proc. 23 (1975) 575 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Strings in SO(10), Phys. Lett. B 113 (1982) 237 [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Walls Bounded by Strings, Phys. Rev. D 26 (1982) 435 [INSPIRE].
G. Lazarides and Q. Shafi, Superconducting membranes, Phys. Lett. B 159 (1985) 261 [INSPIRE].
J.T. Mäkinen et al., Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid3He, Nature Commun. 10 (2019) 237 [arXiv:1807.04328] [INSPIRE].
W. Buchmuller, V. Domcke, H. Murayama and K. Schmitz, Probing the scale of grand unification with gravitational waves, Phys. Lett. B 809 (2020) 135764 [arXiv:1912.03695] [INSPIRE].
W. Buchmuller, V. Domcke and K. Schmitz, From NANOGrav to LIGO with metastable cosmic strings, Phys. Lett. B 811 (2020) 135914 [arXiv:2009.10649] [INSPIRE].
L. Sousa, P.P. Avelino and G.S.F. Guedes, Full analytical approximation to the stochastic gravitational wave background generated by cosmic string networks, Phys. Rev. D 101 (2020) 103508 [arXiv:2002.01079] [INSPIRE].
J.J. Blanco-Pillado, K.D. Olum and J.M. Wachter, Comparison of cosmic string and superstring models to NANOGrav 12.5-year results, Phys. Rev. D 103 (2021) 103512 [arXiv:2102.08194] [INSPIRE].
G. Lazarides, R. Maji and Q. Shafi, Cosmic strings, inflation, and gravity waves, Phys. Rev. D 104 (2021) 095004 [arXiv:2104.02016] [INSPIRE].
W. Buchmuller, V. Domcke and K. Schmitz, Stochastic gravitational-wave background from metastable cosmic strings, JCAP 12 (2021) 006 [arXiv:2107.04578] [INSPIRE].
J. Chakrabortty, G. Lazarides, R. Maji and Q. Shafi, Primordial Monopoles and Strings, Inflation, and Gravity Waves, JHEP 02 (2021) 114 [arXiv:2011.01838] [INSPIRE].
S.F. King, S. Pascoli, J. Turner and Y.-L. Zhou, Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories, Phys. Rev. Lett. 126 (2021) 021802 [arXiv:2005.13549] [INSPIRE].
S.F. King, S. Pascoli, J. Turner and Y.-L. Zhou, Confronting SO(10) GUTs with proton decay and gravitational waves, JHEP 10 (2021) 225 [arXiv:2106.15634] [INSPIRE].
G. Lazarides, R. Maji and Q. Shafi, Gravitational waves from quasi-stable strings, JCAP 08 (2022) 042 [arXiv:2203.11204] [INSPIRE].
A. Afzal, W. Ahmed, M.U. Rehman and Q. Shafi, μ-hybrid inflation, gravitino dark matter, and stochastic gravitational wave background from cosmic strings, Phys. Rev. D 105 (2022) 103539 [arXiv:2202.07386] [INSPIRE].
Z.A. Borboruah and U.A. Yajnik, Left-Right Symmetry Breaking and Gravitational Waves: A Tale of Two Phase Transitions, arXiv:2212.05829 [INSPIRE].
D. Borah and A. Dasgupta, Probing left-right symmetry via gravitational waves from domain walls, Phys. Rev. D 106 (2022) 035016 [arXiv:2205.12220] [INSPIRE].
P. Banerjee and U.A. Yajnik, Gravitational wave signature of generic disappearance of Z2-symmetry breaking domain walls, arXiv:2303.02593 [INSPIRE].
A.E. Everett and A. Vilenkin, Left-right Symmetric Theories and Vacuum Domain Walls and Strings, Nucl. Phys. B 207 (1982) 43 [INSPIRE].
D.I. Dunsky et al., GUTs, hybrid topological defects, and gravitational waves, Phys. Rev. D 106 (2022) 075030 [arXiv:2111.08750] [INSPIRE].
R. Jeannerot, J. Rocher and M. Sakellariadou, How generic is cosmic string formation in SUSY GUTs, Phys. Rev. D 68 (2003) 103514 [hep-ph/0308134] [INSPIRE].
G. Lazarides and Q. Shafi, Monopoles, Strings, and Necklaces in SO(10) and E6, JHEP 10 (2019) 193 [arXiv:1904.06880] [INSPIRE].
G. Lazarides and Q. Shafi, Extended Structures at Intermediate Scales in an Inflationary Cosmology, Phys. Lett. B 148 (1984) 35 [INSPIRE].
V.N. Şenoğuz and Q. Shafi, Primordial monopoles, proton decay, gravity waves and GUT inflation, Phys. Lett. B 752 (2016) 169 [arXiv:1510.04442] [INSPIRE].
R. Maji and Q. Shafi, Monopoles, strings and gravitational waves in non-minimal inflation, JCAP 03 (2023) 007 [arXiv:2208.08137] [INSPIRE].
G.E. Volovik, Composite topological objects in topological superfluids, J. Exp. Theor. Phys. 131 (2020) 11 [arXiv:1912.05962] [INSPIRE].
G.E. Volovik and K. Zhang, String monopoles, string walls, vortex skyrmions, and nexus objects in the polar distorted B phase of 3He, Phys. Rev. Res. 2 (2020) 023263 [arXiv:2002.07578] [INSPIRE].
J.T. Mäkinen, K. Zhang and V.B. Eltsov, Vortex-bound solitons in topological superfluid 3He, J. Phys. Condens. Matter 35 (2023) 214001 [arXiv:2211.17117] [INSPIRE].
A. Vilenkin, Cosmological evolution of monopoles connected by strings, Nucl. Phys. B 196 (1982) 240 [INSPIRE].
M. Hindmarsh and T.W.B. Kibble, Beads on strings, Phys. Rev. Lett. 55 (1985) 2398 [INSPIRE].
M. Aryal and A.E. Everett, Properties of Z(2) Strings, Phys. Rev. D 35 (1987) 3105 [INSPIRE].
T.W.B. Kibble and T. Vachaspati, Monopoles on strings, J. Phys. G 42 (2015) 094002 [arXiv:1506.02022] [INSPIRE].
A. De Rujula, H. Georgi and S.L. Glashow, Flavor goniometry by proton decay, Phys. Rev. Lett. 45 (1980) 413 [INSPIRE].
S.M. Barr, A New Symmetry Breaking Pattern for SO(10) and Proton Decay, Phys. Lett. B 112 (1982) 219 [INSPIRE].
J. Chakrabortty and A. Raychaudhuri, GUTs with dim-5 interactions: Gauge Unification and Intermediate Scales, Phys. Rev. D 81 (2010) 055004 [arXiv:0909.3905] [INSPIRE].
J. Chakrabortty et al., Roadmap of left-right models based on GUTs, Phys. Rev. D 97 (2018) 095010 [arXiv:1711.11391] [INSPIRE].
J. Chakrabortty, R. Maji and S.F. King, Unification, Proton Decay and Topological Defects in non-SUSY GUTs with Thresholds, Phys. Rev. D 99 (2019) 095008 [arXiv:1901.05867] [INSPIRE].
R. Holman, G. Lazarides and Q. Shafi, Axions and the Dark Matter of the Universe, Phys. Rev. D 27 (1983) 995 [INSPIRE].
T. Ohlsson, M. Pernow and E. Sönnerlind, Realizing unification in two different SO(10) models with one intermediate breaking scale, Eur. Phys. J. C 80 (2020) 1089 [arXiv:2006.13936] [INSPIRE].
M. Kadastik, K. Kannike and M. Raidal, Matter parity as the origin of scalar Dark Matter, Phys. Rev. D 81 (2010) 015002 [arXiv:0903.2475] [INSPIRE].
Y. Mambrini et al., Dark matter and gauge coupling unification in nonsupersymmetric SO(10) grand unified models, Phys. Rev. D 91 (2015) 095010 [arXiv:1502.06929] [INSPIRE].
S.M. Boucenna, M.B. Krauss and E. Nardi, Dark matter from the vector of SO (10), Phys. Lett. B 755 (2016) 168 [arXiv:1511.02524] [INSPIRE].
S. Ferrari, T. Hambye, J. Heeck and M.H.G. Tytgat, SO(10) paths to dark matter, Phys. Rev. D 99 (2019) 055032 [arXiv:1811.07910] [INSPIRE].
G. Lazarides and Q. Shafi, Axion Model with Intermediate Scale Fermionic Dark Matter, Phys. Lett. B 807 (2020) 135603 [arXiv:2004.11560] [INSPIRE].
N. Okada, D. Raut and Q. Shafi, Axions, WIMPs, proton decay and observable r in SO(10), Eur. Phys. J. C 83 (2023) 273 [arXiv:2207.10538] [INSPIRE].
G. Lazarides, R. Maji, R. Roshan and Q. Shafi, A predictive SO(10) model, JCAP 12 (2022) 009 [arXiv:2210.03710] [INSPIRE].
A. Stern and U.A. Yajnik, SO(10) Vortices and the Electroweak Phase Transition, Nucl. Phys. B 267 (1986) 158 [INSPIRE].
R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [INSPIRE].
M. Daniel, G. Lazarides and Q. Shafi, SU(5) Monopoles, Magnetic Symmetry and Confinement, Nucl. Phys. B 170 (1980) 156 [INSPIRE].
C.P. Dokos and T.N. Tomaras, Monopoles and Dyons in the SU(5) Model, Phys. Rev. D 21 (1980) 2940 [INSPIRE].
G. Lazarides and Q. Shafi, Triply Charged Monopole and Magnetic Quarks, Phys. Lett. B 818 (2021) 136363 [arXiv:2101.01412] [INSPIRE].
C.L. Gardner and J.A. Harvey, Stable Grand Unified Monopoles With Multiple Dirac Charge, Phys. Rev. Lett. 52 (1984) 879 [INSPIRE].
T. Vachaspati, An Attempt to construct the Standard Model with monopoles, Phys. Rev. Lett. 76 (1996) 188 [hep-ph/9509271] [INSPIRE].
G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
A.M. Polyakov, Particle Spectrum in Quantum Field Theory, JETP Lett. 20 (1974) 194 [INSPIRE].
G. Lazarides, M. Magg and Q. Shafi, Phase Transitions and Magnetic Monopoles in SO(10), Phys. Lett. B 97 (1980) 87 [INSPIRE].
A.E. Everett and M. Aryal, Comment on ‘Monopoles on strings.’, Phys. Rev. Lett. 57 (1986) 646 [INSPIRE].
J.A. Dror et al., Testing the Seesaw Mechanism and Leptogenesis with Gravitational Waves, Phys. Rev. Lett. 124 (2020) 041804 [arXiv:1908.03227] [INSPIRE].
Acknowledgments
A.T. is partially supported by the Bartol Research Institute, University of Delaware. The work of G.L. and Q.S. is supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “First Call for H.F.R.I. Research Projects to support Faculty Members and Researchers and the procurement of high-cost research equipment grant” (Project Number:2251). Q.S. thanks Rinku Maji and Anish Ghoshal for useful discussions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2303.15159
Rights and permissions
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.
About this article
Cite this article
Lazarides, G., Shafi, Q. & Tiwari, A. Composite topological structures in SO(10). J. High Energ. Phys. 2023, 119 (2023). https://doi.org/10.1007/JHEP05(2023)119
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)119