Abstract
We show that spectral walls are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol’nyi-Prasad-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. We also show that spectral walls appear as singularities of the dynamical vibrational moduli space.
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P.G. Kevrekidis and R.H. Goodman, Four decades of kink interactions in nonlinear Klein-Gordon models: a crucial typo, recent developments and the challenges ahead, arXiv:1909.03128 [INSPIRE].
N.S. Manton, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Collective coordinate model of kink-antikink collisions in ϕ4 theory, Phys. Rev. Lett. 127 (2021) 071601 [arXiv:2106.05153] [INSPIRE].
N.S. Manton, A remark on the scattering of BPS monopoles, Phys. Lett. B 110 (1982) 54 [INSPIRE].
N.S. Manton and P. Sutcliffe, Topological solitons, Cambridge University Press, Cambridge U.K. (2004).
N.S. Manton, Unstable manifolds and soliton dynamics, Phys. Rev. Lett. 60 (1988) 1916 [INSPIRE].
C. Adam, T. Romanczukiewicz and A. Wereszczynski, The ϕ4 model with the BPS preserving defect, JHEP 03 (2019) 131 [arXiv:1812.04007] [INSPIRE].
C. Adam, K. Oles, J.M. Queiruga, T. Romanczukiewicz and A. Wereszczynski, Solvable self-dual impurity models, JHEP 07 (2019) 150 [arXiv:1905.06080] [INSPIRE].
C. Adam, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Spectral walls in soliton collisions, Phys. Rev. Lett. 122 (2019) 241601 [arXiv:1903.12100] [INSPIRE].
C. Adam, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Kink-antikink scattering in the ϕ4 model without static intersoliton forces, Phys. Rev. D 101 (2020) 105021 [arXiv:1909.06901] [INSPIRE].
C. Montonen, On solitons with an abelian charge in scalar field theories. 1. Classical theory and Bohr-Sommerfeld quantization, Nucl. Phys. B 112 (1976) 349 [INSPIRE].
S. Sarkar, S.E. Trullinger and A.R. Bishop, Solitary wave solution for a complex one-dimensional field, Phys. Lett. A 59 (1976) 255 [INSPIRE].
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].
J.D. Edelstein, M.L. Trobo, F.A. Brito and D. Bazeia, Kinks inside supersymmetric domain ribbons, Phys. Rev. D 57 (1998) 7561 [hep-th/9707016] [INSPIRE].
D. Bazeia, J.R.S. Nascimento, R.F. Ribeiro and D. Toledo, Soliton stability in systems of two real scalar fields, J. Phys. A 30 (1997) 8157 [hep-th/9705224] [INSPIRE].
A.A. Izquierdo, M.A.G. Leon and J.M. Guilarte, The kink variety in systems of two coupled scalar fields in two space-time dimensions, Phys. Rev. D 65 (2002) 085012 [hep-th/0201200] [INSPIRE].
A.A. Izquierdo, M.A. Gonzalez Leon, J.M. Guilarte and M. de la Torre Mayado, Adiabatic motion of two component BPS kinks, Phys. Rev. D 66 (2002) 105022 [hep-th/0207064] [INSPIRE].
D. Bazeia, L. Losano and C. Wotzasek, Domain walls in three field models, Phys. Rev. D 66 (2002) 105025 [hep-th/0206031] [INSPIRE].
D. Bazeia, J. Menezes and M.M. Santos, Complete factorization of equations of motion in supersymmetric field theories, Nucl. Phys. B 636 (2002) 132 [hep-th/0103041] [INSPIRE].
A. Alonso-Izquierdo and J. Mateos Guilarte, Generalized MSTB Models: Structure and kink varieties, Physica D237 (2008) 3263.
A. Alonso-Izquierdo, Non-topological kink scattering in a two-component scalar field theory model, Comm. Nonlin. Sci. Numer. Simul. 85 (2020) 105251.
M.A. Shifman and M.B. Voloshin, Degenerate domain wall solutions in supersymmetric theories, Phys. Rev. D 57 (1998) 2590 [hep-th/9709137] [INSPIRE].
A. Alonso-Izquierdo, Kink dynamics in a system of two coupled scalar fields in two spacetime dimensions, Physica D 365 (2018) 12.
L.A. Ferreira, P. Klimas and W.J. Zakrzewski, Self-dual sectors for scalar field theories in (1 + 1) dimensions, JHEP 01 (2019) 020 [arXiv:1808.10052] [INSPIRE].
L.A. Ferreira, P. Klimas, A. Wereszczynski and W.J. Zakrzewski, Some comments on BPS systems, J. Phys. A 52 (2019) 315201.
G. Luchini and T. Tassis, BPS states for scalar field theories based on \( \mathfrak{g} \)2 and \( \mathfrak{su} \)(4) algebras, JHEP 05 (2020) 011 [arXiv:1909.04467] [INSPIRE].
D. Bazeia, M.A. Liao and M.A. Marques, Geometrically constrained kinklike configurations, Eur. Phys. J. Plus. 135 (2020) 383.
S. Pnevmatikos, Soliton dynamics of hydrogen-bonded networks: a mechanism for proton conductivity, Phys. Rev. Lett. 60 (1988) 1534.
N.S. Manton, K. Oleś and A. Wereszczyński, Iterated ϕ4 kinks, JHEP 10 (2019) 086 [arXiv:1908.05893] [INSPIRE].
N.S. Manton, K. Oleś, T. Romańczukiewicz and A. Wereszczyński, Kink moduli spaces: Collective coordinates reconsidered, Phys. Rev. D 103 (2021) 025024 [arXiv:2008.01026] [INSPIRE].
D. Tong and K. Wong, Vortices and impurities, JHEP 01 (2014) 090 [arXiv:1309.2644] [INSPIRE].
J. Ashcroft and S. Krusch, Vortices and magnetic impurities, Phys. Rev. D 101 (2020) 025004.
S.B. Gudnason and C. Ross, Magnetic impurities, integrable vortices and the Toda equation, Lett. Math. Phys. 111 (2021) 100 [arXiv:2105.01332] [INSPIRE].
G.W. Gibbons and P.K. Townsend, A Bogomolny equation for intersecting domain walls, Phys. Rev. Lett. 83 (1999) 1727 [hep-th/9905196] [INSPIRE].
D. Bazeia, L. Losano and J.R.L. Santos, Kinklike structures in scalar field theories: from one-field to two-field models, Phys. Lett. A 377 (2013) 1615 [arXiv:1304.6904] [INSPIRE].
J.R.L. Santos, P.H.R.S. Moraes, D.A. Ferreira and D.C.V. Neta, Building analytical three-field cosmological models, Eur. Phys. J. C 78 (2018) 169 [arXiv:1707.02611] [INSPIRE].
S. Otten, K. Rolbiecki, S. Caron, J.-S. Kim, R. Ruiz De Austri and J. Tattersall, DeepXS: Fast approximation of MSSM electroweak cross sections at NLO, Eur. Phys. J. C 80 (2020) 12 [arXiv:1810.08312] [INSPIRE].
M. Peyrard, S. Pnevmatikos and N. Flytzanis, Dynamics of two-component solitary waves in hydrogen-bonded chains, Phys. Rev. A 36 (1987) 903.
A.V. Zolotaryuk, S. Pnevmatikos and A.V. Savin, Charge transport by solitons in hydrogen-bonded materials, Phys. Rev. Lett. 67 (1991) 707.
G.R. Farrar and P.J.E. Peebles, Interacting dark matter and dark energy, Astrophys. J. 604 (2004) 1 [astro-ph/0307316] [INSPIRE].
S. Micheletti, E. Abdalla and B. Wang, A field theory model for dark matter and dark energy in interaction, Phys. Rev. D 79 (2009) 123506 [arXiv:0902.0318] [INSPIRE].
O. Bertolami, P. Carrilho and J. Paramos, Two-scalar-field model for the interaction of dark energy and dark matter, Phys. Rev. D 86 (2012) 103522 [arXiv:1206.2589] [INSPIRE].
V.A. Gani, M.A. Lizunova and R.V. Radomskiy, Scalar triplet on a domain wall: an exact solution, JHEP 04 (2016) 043 [arXiv:1601.07954] [INSPIRE].
A. Alonso-Izquierdo, Reflection, transmutation, annihilation and resonance in two-component kink collisions, Phys. Rev. D 97 (2018) 045016.
J.R. Morris, Interacting kinks and meson mixing, Annals Phys. 400 (2019) 346 [arXiv:1901.01467] [INSPIRE].
A. Alonso-Izquierdo, M.A.G. Leon, J.M. Vaquero and M.d.l.T. Mayado, Kink scattering in a generalized Wess-Zumino model, arXiv:2105.05750 [INSPIRE].
C. Adam, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Kink-antikink collisions in a weakly interacting ϕ4 model, Phys. Rev. E 102 (2020) 062214 [arXiv:1912.09371] [INSPIRE].
C.J. Halcrow, Vibrational quantisation of the B = 7 Skyrmion, Nucl. Phys. B 904 (2016) 106 [arXiv:1511.00682] [INSPIRE].
S. Bjarke Gudnason and C. Halcrow, Vibrational modes of Skyrmions, Phys. Rev. D 98 (2018) 125010 [arXiv:1811.00562] [INSPIRE].
C. Halcrow, Quantum soliton scattering manifolds, JHEP 07 (2020) 182 [arXiv:2004.14167] [INSPIRE].
J. Evslin, Well-defined quantum soliton masses without supersymmetry, Phys. Rev. D 101 (2020) 065005.
J. Evslin, Normal ordering normal modes, Eur. Phys. J. C 81 (2021) 92 [arXiv:2007.05741] [INSPIRE].
J. Evslin, Evidence for the unbinding of the ϕ4 kink’s shape mode, arXiv:2104.14387 [INSPIRE].
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Adam, C., Oles, K., Romanczukiewicz, T. et al. Spectral walls in multifield kink dynamics. J. High Energ. Phys. 2021, 147 (2021). https://doi.org/10.1007/JHEP08(2021)147
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DOI: https://doi.org/10.1007/JHEP08(2021)147