Abstract
In this paper we initiate the study of correlation functions of a single trace operator and a circular supersymmetric Wilson loop in ABJM theory. The single trace operator is in the scalar sector and is an eigenstate of the planar two-loop dilatation operator. The Wilson loop is in the fundamental representation of the gauge group or a suitable (super-)group. Such correlation functions at tree level can be written as an overlap of the Bethe state corresponding to the single trace operator and a boundary state which corresponds to the Wilson loop. There are various type of supersymmetric Wilson loops in ABJM theory. We show that some of them correspond to tree-level integrable boundary states while some are not. For the tree-level integrable ones, we prove their integrability and obtain analytic formula for the overlaps. For the non-integrable ones, we give examples of non-vanishing overlaps for Bethe states which violate selection rules.
Article PDF
Similar content being viewed by others
References
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for \( \mathcal{N} \) = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
N. Beisert and M. Staudacher, Long-range psu(2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].
Z. Bajnok and R.A. Janik, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys. B 807 (2009) 625 [arXiv:0807.0399] [INSPIRE].
J. Ambjorn, R.A. Janik and C. Kristjansen, Wrapping interactions and a new source of corrections to the spin-chain/string duality, Nucl. Phys. B 736 (2006) 288 [hep-th/0510171] [INSPIRE].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe Ansatz for planar AdS/CFT: A Proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].
N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 103 (2009) 131601 [arXiv:0901.3753] [INSPIRE].
G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS5 × S5 Mirror Model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N} \) = 4 Super-Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
B. Chen, X.-J. Wang and Y.-S. Wu, Integrable open spin chain in superYang-Mills and the plane wave/SYM duality, JHEP 02 (2004) 029 [hep-th/0401016] [INSPIRE].
B. Chen, X.-J. Wang and Y.-S. Wu, Open spin chain and open spinning string, Phys. Lett. B 591 (2004) 170 [hep-th/0403004] [INSPIRE].
T. Erler and N. Mann, Integrable open spin chains and the doubling trick in \( \mathcal{N} \) = 2 SYM with fundamental matter, JHEP 01 (2006) 131 [hep-th/0508064] [INSPIRE].
O. DeWolfe and N. Mann, Integrable open spin chains in defect conformal field theory, JHEP 04 (2004) 035 [hep-th/0401041] [INSPIRE].
D. Berenstein and S.E. Vazquez, Integrable open spin chains from giant gravitons, JHEP 06 (2005) 059 [hep-th/0501078] [INSPIRE].
N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].
D. Correa, M. Leoni and S. Luque, Spin chain integrability in non-supersymmetric Wilson loops, JHEP 12 (2018) 050 [arXiv:1810.04643] [INSPIRE].
M. de Leeuw, C. Kristjansen and K. Zarembo, One-point Functions in Defect CFT and Integrability, JHEP 08 (2015) 098 [arXiv:1506.06958] [INSPIRE].
I. Buhl-Mortensen, M. de Leeuw, C. Kristjansen and K. Zarembo, One-point Functions in AdS/dCFT from Matrix Product States, JHEP 02 (2016) 052 [arXiv:1512.02532] [INSPIRE].
M. De Leeuw, C. Kristjansen and G. Linardopoulos, Scalar one-point functions and matrix product states of AdS/dCFT, Phys. Lett. B 781 (2018) 238 [arXiv:1802.01598] [INSPIRE].
L. Piroli, B. Pozsgay and E. Vernier, What is an integrable quench?, Nucl. Phys. B 925 (2017) 362 [arXiv:1709.04796] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Structure constants in \( \mathcal{N} \) = 4 SYM at finite coupling as worldsheet g-function, JHEP 07 (2020) 037 [arXiv:1906.07733] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Exact Three-Point Functions of Determinant Operators in Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 123 (2019) 191601 [arXiv:1907.11242] [INSPIRE].
C. Kristjansen and K. Zarembo, ’t Hooft loops and integrability, JHEP 08 (2023) 184 [arXiv:2305.03649] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Wilson loops and exact g-functions, to appear.
H. Ouyang and J.-B. Wu, Fermionic Bogomolǹyi-Prasad-Sommerfield Wilson loops in four-dimensional \( \mathcal{N} \) = 2 superconformal gauge theories, SciPost Phys. 14 (2023) 008 [arXiv:2205.01348] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N} \) = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
T. Klose, Review of AdS/CFT Integrability, Chapter IV.3: \( \mathcal{N} \) = 6 Chern-Simons and Strings on AdS4 × CP3, Lett. Math. Phys. 99 (2012) 401 [arXiv:1012.3999] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for superconformal Chern-Simons, JHEP 09 (2008) 040 [arXiv:0806.3951] [INSPIRE].
D. Bak and S.-J. Rey, Integrable Spin Chain in Superconformal Chern-Simons Theory, JHEP 10 (2008) 053 [arXiv:0807.2063] [INSPIRE].
N. Gromov and P. Vieira, The all loop AdS4/CFT3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [INSPIRE].
N. Gromov and G. Sizov, Exact Slope and Interpolating Functions in \( \mathcal{N} \) = 6 Supersymmetric Chern-Simons Theory, Phys. Rev. Lett. 113 (2014) 121601 [arXiv:1403.1894] [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum Spectral Curve of the \( \mathcal{N} \) = 6 Supersymmetric Chern-Simons Theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional \( \mathcal{N} \) = 6 supersymmetric Chern-Simons Theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [INSPIRE].
B. Chen and J.-B. Wu, Supersymmetric Wilson Loops in \( \mathcal{N} \) = 6 Super Chern-Simons-matter theory, Nucl. Phys. B 825 (2010) 38 [arXiv:0809.2863] [INSPIRE].
S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual, JHEP 03 (2009) 127 [arXiv:0809.3786] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
M. Marino and P. Putrov, Exact Results in ABJM Theory from Topological Strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].
N. Bai et al., Integrable Open Spin Chains from Flavored ABJM Theory, JHEP 08 (2017) 001 [arXiv:1704.05807] [INSPIRE].
D.H. Correa, V.I. Giraldo-Rivera and M. Lagares, Integrable Wilson loops in ABJM: a Y-system computation of the cusp anomalous dimension, JHEP 06 (2023) 179 [arXiv:2304.01924] [INSPIRE].
T. Bargheer and F. Lobbert, unpublished.
C. Ahn and D. Correa, unpublished.
N. Drukker et al., Roadmap on Wilson loops in 3d Chern-Simons-matter theories, J. Phys. A 53 (2020) 173001 [arXiv:1910.00588] [INSPIRE].
H.-H. Chen, H. Ouyang and J.-B. Wu, Open Spin Chains from Determinant Like Operators in ABJM Theory, Phys. Rev. D 98 (2018) 106012 [arXiv:1809.09941] [INSPIRE].
N. Bai, H.-H. Chen, H. Ouyang and J.-B. Wu, Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton, JHEP 03 (2019) 193 [arXiv:1901.03949] [INSPIRE].
H.-H. Chen, Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton, JHEP 08 (2019) 109 [arXiv:1906.09886] [INSPIRE].
P. Yang, Y. Jiang, S. Komatsu and J.-B. Wu, Three-point functions in ABJM and Bethe Ansatz, JHEP 01 (2022) 002 [arXiv:2103.15840] [INSPIRE].
C. Kristjansen, D.-L. Vu and K. Zarembo, Integrable domain walls in ABJM theory, JHEP 02 (2022) 070 [arXiv:2112.10438] [INSPIRE].
G. Linardopoulos and K. Zarembo, String integrability of defect CFT and dynamical reflection matrices, JHEP 05 (2021) 203 [arXiv:2102.12381] [INSPIRE].
G. Linardopoulos, String integrability of the ABJM defect, JHEP 06 (2022) 033 [arXiv:2202.06824] [INSPIRE].
T. Gombor and Z. Bajnok, Boundary states, overlaps, nesting and bootstrapping AdS/dCFT, JHEP 10 (2020) 123 [arXiv:2004.11329] [INSPIRE].
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
A. Lewkowycz and J. Maldacena, Exact results for the entanglement entropy and the energy radiated by a quark, JHEP 05 (2014) 025 [arXiv:1312.5682] [INSPIRE].
N. Drukker and D. Trancanelli, A Supermatrix model for \( \mathcal{N} \) = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].
H. Ouyang, J.-B. Wu and J.-J. Zhang, Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories, Phys. Lett. B 753 (2016) 215 [arXiv:1510.05475] [INSPIRE].
H. Ouyang, J.-B. Wu and J.-J. Zhang, Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories, Nucl. Phys. B 910 (2016) 496 [arXiv:1511.02967] [INSPIRE].
D.H. Correa, V.I. Giraldo-Rivera and G.A. Silva, Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations, JHEP 03 (2020) 010 [arXiv:1910.04225] [INSPIRE].
N. Drukker and Z. Kong, 1/3 BPS loops and defect CFTs in ABJM theory, JHEP 06 (2023) 137 [arXiv:2212.03886] [INSPIRE].
N. Drukker, BPS Wilson loops and quiver varieties, J. Phys. A 53 (2020) 385402 [arXiv:2004.11393] [INSPIRE].
T. Gombor, Integrable crosscap states in \( \mathfrak{gl}(N) \) spin chains, JHEP 10 (2022) 096 [arXiv:2207.10598] [INSPIRE].
P. Yang, Integrable Boundary States in ABJM Theory, arXiv:2208.12010 [INSPIRE].
T. Gombor, On exact overlaps for \( \mathfrak{gl}(N) \) symmetric spin chains, Nucl. Phys. B 983 (2022) 115909 [arXiv:2110.07960] [INSPIRE].
T. Gombor and C. Kristjansen, Overlaps for matrix product states of arbitrary bond dimension in ABJM theory, Phys. Lett. B 834 (2022) 137428 [arXiv:2207.06866] [INSPIRE].
T. Gombor and Z. Bajnok, Boundary state bootstrap and asymptotic overlaps in AdS/dCFT, JHEP 03 (2021) 222 [arXiv:2006.16151] [INSPIRE].
C. Kristjansen, D. Müller and K. Zarembo, Overlaps and fermionic dualities for integrable super spin chains, JHEP 03 (2021) 100 [arXiv:2011.12192] [INSPIRE].
C. Kristjansen, D. Müller and K. Zarembo, Duality relations for overlaps of integrable boundary states in AdS/dCFT, JHEP 09 (2021) 004 [arXiv:2106.08116] [INSPIRE].
S. Komatsu and Y. Wang, Non-perturbative defect one-point functions in planar \( \mathcal{N} \) = 4 super-Yang-Mills, Nucl. Phys. B 958 (2020) 115120 [arXiv:2004.09514] [INSPIRE].
S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson Loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].
J. Gomis and F. Passerini, Wilson Loops as D3-Branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].
L. Castiglioni, S. Penati, M. Tenser and D. Trancanelli, Interpolating Wilson loops and enriched RG flows, JHEP 08 (2023) 106 [arXiv:2211.16501] [INSPIRE].
V. Cardinali, L. Griguolo, G. Martelloni and D. Seminara, New supersymmetric Wilson loops in ABJ(M) theories, Phys. Lett. B 718 (2012) 615 [arXiv:1209.4032] [INSPIRE].
M.S. Bianchi et al., BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis, JHEP 06 (2014) 123 [arXiv:1402.4128] [INSPIRE].
S. Giombi and V. Pestun, Correlators of local operators and 1/8 BPS Wilson loops on S2 from 2d YM and matrix models, JHEP 10 (2010) 033 [arXiv:0906.1572] [INSPIRE].
S. Giombi and V. Pestun, Correlators of Wilson Loops and Local Operators from Multi-Matrix Models and Strings in AdS, JHEP 01 (2013) 101 [arXiv:1207.7083] [INSPIRE].
S. Giombi, J. Jiang and S. Komatsu, Giant Wilson loops and AdS2/dCFT1, JHEP 11 (2020) 064 [arXiv:2005.08890] [INSPIRE].
D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The Operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].
S. Giombi, R. Ricci and D. Trancanelli, Operator product expansion of higher rank Wilson loops from D-branes and matrix models, JHEP 10 (2006) 045 [hep-th/0608077] [INSPIRE].
K. Zarembo, Open string fluctuations in AdS5 × S5 and operators with large R charge, Phys. Rev. D 66 (2002) 105021 [hep-th/0209095] [INSPIRE].
L. Guerrini, On protected defect correlators in 3d \( \mathcal{N} \) ≥ 4 theories, arXiv:2301.07035 [INSPIRE].
H. Ouyang, J.-B. Wu and J.-J. Zhang, BPS Wilson loops in Minkowski spacetime and Euclidean space, Eur. Phys. J. C 75 (2015) 606 [arXiv:1504.06929] [INSPIRE].
D. Gaiotto, S. Giombi and X. Yin, Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory, JHEP 04 (2009) 066 [arXiv:0806.4589] [INSPIRE].
K. Hosomichi et al., \( \mathcal{N} \) = 5, 6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].
S. Terashima, On M5-branes in \( \mathcal{N} \) = 6 Membrane Action, JHEP 08 (2008) 080 [arXiv:0807.0197] [INSPIRE].
M.A. Bandres, A.E. Lipstein and J.H. Schwarz, Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry, JHEP 09 (2008) 027 [arXiv:0807.0880] [INSPIRE].
H. Nicolai, A possible constructive approach to (super-ϕ3)4: (I). Euclidean formulation of the model, Nucl. Phys. B 140 (1978) 294 [INSPIRE].
C. Marboe and D. Volin, Fast analytic solver of rational Bethe equations, J. Phys. A 50 (2017) 204002 [arXiv:1608.06504] [INSPIRE].
J. Gu, Y. Jiang and M. Sperling, Rational Q-systems, Higgsing and Mirror Symmetry, SciPost Phys. 14 (2023) 034 [arXiv:2208.10047] [INSPIRE].
Acknowledgments
We would like to thank Bin Chen for collaboration at early stages of this project, Hong-Fei Shu, Jiaju Zhang for help discussions, and Zhi-Xin Hu for helps on using the computer cluster at CJQS, TJU. Y.J. would like to thank Center for Joint Quantum Studies of Tianjin University for hospitality during the final stage of the work. The work of Y.J. is partly supported by Startup Funding no. 3207022217A1 of Southeast University. The work of J.W. and P.Y. is partly supported by the National Natural Science Foundation of China, Grant No. 11975164, 11935009, 12375066, 12247103, 12047502, and Natural Science Foundation of Tianjin under Grant No. 20JCYBJC00910.
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: 2306.05773
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
Jiang, Y., Wu, JB. & Yang, P. Wilson-loop one-point functions in ABJM theory. J. High Energ. Phys. 2023, 47 (2023). https://doi.org/10.1007/JHEP09(2023)047
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2023)047