Abstract
Ref. [J. High Energy Phys. 1708, 001 (2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena (ABJM) theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001 (2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.
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N. Beisert, C. Ahn, L. F. Alday, Z. Bajnok, J. M. Drummond, L. Freyhult, N. Gromov, R. A. Janik, V. Kazakov, T. Klose, G. P. Korchemsky, C. Kristjansen, M. Magro, T. McLoughlin, J. A. Minahan, R. I. Nepomechie, A. Rej, R. Roiban, S. Schafer-Nameki, C. Sieg, M. Staudacher, A. Torrielli, A. A. Tseytlin, P. Vieira, D. Volin, and K. Zoubos, Lett. Math. Phys. 99, 3 (2012), arXiv: 1012.3982.
L. Brink, J. H. Schwarz, and J. Scherk, Nucl. Phys. B 121, 77 (1977).
O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, J. High Energy Phys. 2008, 091 (2008), arXiv: 0806.1218.
J. A. Minahan, and K. Zarembo, J. High Energy Phys. 2003, 13 (2003).
J. A. Minahan, and K. Zarembo, J. High Energy Phys. 2008, 40 (2008), arXiv: 0806.3951.
D. Bak, and S. J. Rey, J. High Energy Phys. 2008, 53 (2008), arXiv: 0807.2063.
A. Karch, and E. Katz, J. High Energy Phys. 2002, 43 (2002).
S. Hohenegger, and I. Kirsch, J. High Energy Phys. 2009, 129 (2009), arXiv: 0903.1730.
D. Gaiotto, and D. L. Jafferis, J. High Energy Phys. 2012, 15 (2012), arXiv: 0903.2175.
Y. Hikida, W. Li, and T. Takayanagi, J. High Energy Phys. 2009, 65 (2009), arXiv: 0903.2194.
B. A. Burrington, J. T. Liu, L. A. P. Zayas, and D. Vaman, J. High Energy Phys. 2005, 22 (2005).
I. Kirsch, and D. Vaman, Phys. Rev. D 72, 026007 (2005).
E. Conde, and A. V. Ramallo, J. High Energy Phys. 2011, 99 (2011), arXiv: 1105.6045.
B. Chen, X. J. Wang, and Y. S. Wu, J. High Energy Phys. 2004, 29 (2004).
B. Chen, X. J. Wang, and Y. S. Wu, Phys. Lett. B 591, 170 (2004).
T. G. Erler, and N. Mann, J. High Energy Phys. 2006, 131 (2006).
N. Bai, H. H. Chen, S. He, J. B. Wu, W. L. Yang, and M. Q. Zhu, J. High Energy Phys. 2017, 1 (2017), arXiv: 1704.05807.
D. Giataganas, and K. Zoubos, J. High Energ. Phys. 2017, 42 (2017), arXiv: 1707.04033.
C. Ahn, and R. I. Nepomechie, J. High Energy Phys. 2009, 144 (2009), arXiv: 0901.3334.
Y. Y. Li, J. Cao, W. L. Yang, K. Shi, and Y. Wang, Nucl. Phys. B 879, 98 (2014), arXiv: 1311.0432.
I. V. Cherednik, Theor. Math. Phys. 61, 977 (1984) [Teor. Mat. Fiz. 61, 35 (1984)].
E. K. Sklyanin, J. Phys. A-Math. Gen. 21, 2375 (1988).
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Wu, J. Notes on integrable boundary interactions of open SU(4) alternating spin chains. Sci. China Phys. Mech. Astron. 61, 70011 (2018). https://doi.org/10.1007/s11433-018-9190-y
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DOI: https://doi.org/10.1007/s11433-018-9190-y