Abstract
Energy and momentum conservation in the context of a type II, purely transmitting, defect, within a single scalar relativistic two-dimensional field theory, places a severe constraint not only on the nature of the defect but also on the potentials for the scalar fields to either side of it. The constraint is of an unfamiliar type since it requires the Poisson Bracket of the defect contributions to energy and momentum with respect to the defect discontinuity and its conjugate to be balanced by the potential difference across the defect. It is shown that the only solutions to the constraint correspond to the known integrable field theories.
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References
G. Delfino, G. Mussardo and P. Simonetti, Scattering theory and correlation functions in statistical models with a line of defect, Nucl. Phys. B 432 (1994) 518 [hep-th/9409076] [INSPIRE].
R. Konik and A. LeClair, Purely transmitting defect field theories, Nucl. Phys. B 538 (1999) 587 [hep-th/9703085] [INSPIRE].
M. Mintchev, É. Ragoucy and P. Sorba, Scattering in the presence of a reflecting and transmitting impurity, Phys. Lett. B 547 (2002) 313 [hep-th/0209052] [INSPIRE].
P. Bowcock, E. Corrigan and C. Zambon, Classically integrable field theories with defects, in Proceedings of the 6th International Workshop on Conformal Field Theory and Integrable Models, Landau Institute, Chernogolovka, Russia, September 2002 [Int. J. Mod. Phys. A 19S2 (2004) 82] [hep-th/0305022] [INSPIRE].
P. Bowcock, E. Corrigan and C. Zambon, Affine Toda field theories with defects, JHEP 01 (2004) 056 [hep-th/0401020] [INSPIRE].
P. Bowcock, E. Corrigan and C. Zambon, Some aspects of jump-defects in the quantum sine-Gordon model, JHEP 08 (2005) 023 [hep-th/0506169] [INSPIRE].
J.F. Gomes, L.H. Ymai and A.H. Zimerman, The super MKDV and sinh-Gordon hierarchy: solitons and Bäcklund defects, J. Phys. A 39 (2006) 7471 [hep-th/0601014] [INSPIRE].
E. Corrigan and C. Zambon, On purely transmitting defects in affine Toda field theory, JHEP 07 (2007) 001 [arXiv:0705.1066] [INSPIRE].
I. Habibullin and A. Kundu, Quantum and classical integrable sine-Gordon model with defect, Nucl. Phys. B 795 (2008) 549 [arXiv:0709.4611] [INSPIRE].
J.F. Gomes, L.H. Ymai and A.H. Zimerman, Integrablility of a classical N = 2 super sinh-Gordon model with jump defects, JHEP 03 (2008) 001 [arXiv:0710.1391] [INSPIRE].
V. Caudrelier, On a systematic approach to defects in classical integrable field theories, Int. J. Geom. Meth. Mod. Phys. 5 (2008) 1085 [arXiv:0704.2326] [INSPIRE].
E. Corrigan and C. Zambon, A new class of integrable defects, J. Phys. A 42 (2009) 475203 [arXiv:0908.3126] [INSPIRE].
F. Nemes, Semiclassical analysis of defect sine-Gordon theory, Int. J. Mod. Phys. A 25 (2010) 4493 [arXiv:0909.3268] [INSPIRE].
J. Avan and A. Doikou, The sine-Gordon model with integrable defects revisited, JHEP 11 (2012) 008 [arXiv:1205.1661] [INSPIRE].
A.R. Aguirre, J.F. Gomes, N.I. Spano and A.H. Zimerman, N = 1 super sinh-Gordon model with defects revisited, JHEP 02 (2015) 175 [arXiv:1412.2579] [INSPIRE].
A. Doikou, Classical integrable defects as quasi Bäcklund transformations, Nucl. Phys. B 911 (2016) 212 [arXiv:1603.04688] [INSPIRE].
C. Robertson, Folding defect affine Toda field theories, J. Phys. A 47 (2014) 185201 [arXiv:1304.3129] [INSPIRE].
C. Robertson, Defect fusing rules in affine Toda field theory, J. Phys. A 47 (2014) 485205 [arXiv:1408.1960] [INSPIRE].
R. Bristow and P. Bowcock, Momentum conserving defects in affine Toda field theories, JHEP 05 (2017) 153 [arXiv:1612.03002] [INSPIRE].
R. Bristow, Integrability of generalised type-II defects in affine Toda field theory, JHEP 11 (2017) 067 [arXiv:1709.03927] [INSPIRE].
E. Corrigan and C. Zambon, A transmission matrix for a fused pair of integrable defects in the sine-Gordon model, J. Phys. A 43 (2010) 345201 [arXiv:1006.0939] [INSPIRE].
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ArXiv ePrint: 1807.05747
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Corrigan, E., Zambon, C. Type II defects revisited. J. High Energ. Phys. 2018, 19 (2018). https://doi.org/10.1007/JHEP09(2018)019
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DOI: https://doi.org/10.1007/JHEP09(2018)019