Abstract
We study three-point functions of operators on the 1/2 BPS Wilson loop in planar \( \mathcal{N} \) = 4 super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the \( \mathrm{S}\mathrm{L}\left(2,\mathbb{R}\right) \) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.
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References
M. Billo, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
A. Gadde, Conformal constraints on defects, arXiv:1602.06354 [INSPIRE].
N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].
D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve for a cusped Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP 04 (2016) 134 [arXiv:1510.02098] [INSPIRE].
M. Cooke, A. Dekel and N. Drukker, The Wilson loop CFT: insertion dimensions and structure constants from wavy lines, J. Phys. A 50 (2017) 335401 [arXiv:1703.03812] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS 2 /CFT 1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, The cusp anomalous dimension at three loops and beyond, JHEP 05 (2012) 098 [arXiv:1203.1019] [INSPIRE].
A. Cavaglia, N. Gromov and F. Levkovich-Maslyuk, to appear.
N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].
J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].
N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].
N. Drukker and J. Plefka, The structure of n-point functions of chiral primary operators in N = 4 super Yang-Mills at one-loop, JHEP 04 (2009) 001 [arXiv:0812.3341] [INSPIRE].
S. Giombi, C. Sleight and M. Taronna, Spinning AdS loop diagrams: two point functions, arXiv:1708.08404 [INSPIRE].
J.K. Erickson, G.W. Semenoff, R.J. Szabo and K. Zarembo, Static potential in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 61 (2000) 105006 [hep-th/9911088] [INSPIRE].
M. Kim and N. Kiryu, Structure constants of operators on the Wilson loop from integrability, JHEP 11 (2017) 116 [arXiv:1706.02989] [INSPIRE].
Z. Bajnok and L. Hollo, On form factors of boundary changing operators, Nucl. Phys. B 905 (2016) 96 [arXiv:1510.08232] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in \( \mathcal{N} \) = 4 SYM, JHEP 12 (2016) 122 [arXiv:1601.05679] [INSPIRE].
O. Gurdogan and V. Kazakov, New integrable 4D quantum field theories from strongly deformed planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 117 (2016) 201602 [arXiv:1512.06704] [INSPIRE].
J. Caetano, O. Gurdogan and V. Kazakov, Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs, arXiv:1612.05895 [INSPIRE].
O. Mamroud and G. Torrents, RG stability of integrable fishnet models, JHEP 06 (2017) 012 [arXiv:1703.04152] [INSPIRE].
D. Chicherin, V. Kazakov, F. Loebbert, D. Müller and D.-l. Zhong, Yangian symmetry for bi-scalar loop amplitudes, arXiv:1704.01967 [INSPIRE].
N. Gromov et al., Integrability of conformal fishnet theory, arXiv:1706.04167 [INSPIRE].
D. Chicherin et al., Yangian symmetry for fishnet Feynman graphs, arXiv:1708.00007 [INSPIRE].
D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP 05 (2017) 092 [arXiv:1702.08016] [INSPIRE].
D.J. Gross and V. Rosenhaus, A line of CFTs: from generalized free fields to SYK, JHEP 07 (2017) 086 [arXiv:1706.07015] [INSPIRE].
N. Beisert, C. Kristjansen, J. Plefka, G.W. Semenoff and M. Staudacher, BMN correlators and operator mixing in N = 4 super Yang-Mills theory, Nucl. Phys. B 650 (2003) 125 [hep-th/0208178] [INSPIRE].
N.I. Usyukina and A.I. Davydychev, An approach to the evaluation of three and four point ladder diagrams, Phys. Lett. B 298 (1993) 363 [INSPIRE].
C. Chamon, R. Jackiw, S.-Y. Pi and L. Santos, Conformal quantum mechanics as the CFT 1 dual to AdS 2, Phys. Lett. B 701 (2011) 503 [arXiv:1106.0726] [INSPIRE].
S.H. Dong and R. Lemus, A new dynamical group approach to the modified Poschl-Teller potential, quant-ph/0110157.
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ArXiv ePrint: 1710.07325
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Kim, M., Kiryu, N., Komatsu, S. et al. Structure constants of defect changing operators on the 1/2 BPS Wilson loop. J. High Energ. Phys. 2017, 55 (2017). https://doi.org/10.1007/JHEP12(2017)055
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DOI: https://doi.org/10.1007/JHEP12(2017)055