Abstract
We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/\( \sqrt{\lambda } \) held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the two-point function of large charge insertions by evaluating the on-shell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank-1 \( \mathcal{N} \) = 2 superconformal field theories, but our results hold also for non-extremal cases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A Semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP 12 (2015) 071 [arXiv:1505.01537] [INSPIRE].
A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data, JHEP 06 (2017) 011 [arXiv:1611.02912] [INSPIRE].
L. Álvarez-Gaumé, O. Loukas, D. Orlando and S. Reffert, Compensating strong coupling with large charge, JHEP 04 (2017) 059 [arXiv:1610.04495] [INSPIRE].
D. Jafferis, B. Mukhametzhanov and A. Zhiboedov, Conformal Bootstrap At Large Charge, JHEP 05 (2018) 043 [arXiv:1710.11161] [INSPIRE].
L.A. Gaumé, D. Orlando and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rept. 933 (2021) 2180 [arXiv:2008.03308] [INSPIRE].
N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
S. Giombi, J. Jiang and S. Komatsu, Giant Wilson loops and AdS2/dCFT1, JHEP 11 (2020) 064 [arXiv:2005.08890] [INSPIRE].
S. Giombi and S. Komatsu, Exact Correlators on the Wilson Loop in \( \mathcal{N} \) = 4 SYM: Localization, Defect CFT, and Integrability, JHEP 05 (2018) 109 [Erratum ibid. 11 (2018) 123] [arXiv:1802.05201] [INSPIRE].
S. Giombi and S. Komatsu, More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve, J. Phys. A 52 (2019) 125401 [arXiv:1811.02369] [INSPIRE].
P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].
P. Ferrero and C. Meneghelli, Bootstrapping the half-BPS line defect CFT in N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 104 (2021) L081703 [arXiv:2103.10440] [INSPIRE].
J. Barrat, A. Gimenez-Grau and P. Liendo, Bootstrapping holographic defect correlators in \( \mathcal{N} \) = 4 super Yang-Mills, arXiv:2108.13432 [INSPIRE].
N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].
N. Kiryu and S. Komatsu, Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization, JHEP 02 (2019) 090 [arXiv:1812.04593] [INSPIRE].
D. Grabner, N. Gromov and J. Julius, Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve, JHEP 07 (2020) 042 [arXiv:2001.11039] [INSPIRE].
A. Cavaglià, N. Gromov, J. Julius and M. Preti, Integrability and conformal bootstrap: One dimensional defect conformal field theory, Phys. Rev. D 105 (2022) L021902 [arXiv:2107.08510] [INSPIRE].
J. Polchinski and J. Sully, Wilson Loop Renormalization Group Flows, JHEP 10 (2011) 059 [arXiv:1104.5077] [INSPIRE].
M. Beccaria, S. Giombi and A. Tseytlin, Non-supersymmetric Wilson loop in \( \mathcal{N} \) = 4 SYM and defect 1d CFT, JHEP 03 (2018) 131 [arXiv:1712.06874] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Correlators on non-supersymmetric Wilson line in \( \mathcal{N} \) = 4 SYM and AdS2/CFT1, JHEP 05 (2019) 122 [arXiv:1903.04365] [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].
G. Cuomo, Z. Komargodski and A. Raviv-Moshe, Renormalization Group Flows on Line Defects, Phys. Rev. Lett. 128 (2022) 021603 [arXiv:2108.01117] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Higher order RG flow on the Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP 01 (2022) 056 [arXiv:2110.04212] [INSPIRE].
N. Gromov and A. Sever, Analytic Solution of Bremsstrahlung TBA, JHEP 11 (2012) 075 [arXiv:1207.5489] [INSPIRE].
S. Giombi, S. Komatsu and B. Offertaler, Large Charges on the Wilson loop in \( \mathcal{N} \) = 4 SYM II, in preparation.
A. Miwa and T. Yoneya, Holography of Wilson-loop expectation values with local operator insertions, JHEP 12 (2006) 060 [hep-th/0609007] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
P. Yang, Y. Jiang, S. Komatsu and J.-B. Wu, D-branes and Orbit Average, SciPost Phys. 12 (2022) 055 [arXiv:2103.16580] [INSPIRE].
Z. Bajnok, R.A. Janik and A. Wereszczyński, HHL correlators, orbit averaging and form factors, JHEP 09 (2014) 050 [arXiv:1404.4556] [INSPIRE].
A. Grassi, Z. Komargodski and L. Tizzano, Extremal correlators and random matrix theory, JHEP 04 (2021) 214 [arXiv:1908.10306] [INSPIRE].
M. Beccaria, F. Galvagno and A. Hasan, \( \mathcal{N} \) = 2 conformal gauge theories at large R-charge: the SU(N) case, JHEP 03 (2020) 160 [arXiv:2001.06645] [INSPIRE].
N. Gromov, S. Schäfer-Nameki and P. Vieira, Efficient precision quantization in AdS/CFT, JHEP 12 (2008) 013 [arXiv:0807.4752] [INSPIRE].
B. Vicedo, Semiclassical Quantisation of Finite-Gap Strings, JHEP 06 (2008) 086 [arXiv:0803.1605] [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].
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].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, More supersymmetric Wilson loops, Phys. Rev. D 76 (2007) 107703 [arXiv:0704.2237] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Wilson loops: From four-dimensional SYM to two-dimensional YM, Phys. Rev. D 77 (2008) 047901 [arXiv:0707.2699] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Supersymmetric Wilson loops on S3, JHEP 05 (2008) 017 [arXiv:0711.3226] [INSPIRE].
S. Hellerman and S. Maeda, On the Large R-charge Expansion in \( \mathcal{N} \) = 2 Superconformal Field Theories, JHEP 12 (2017) 135 [arXiv:1710.07336] [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 D.J. Gross, An Exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [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].
M. Kim, N. Kiryu, S. Komatsu and T. Nishimura, Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop, JHEP 12 (2017) 055 [arXiv:1710.07325] [INSPIRE].
J. Qiao and S. Rychkov, A tauberian theorem for the conformal bootstrap, JHEP 12 (2017) 119 [arXiv:1709.00008] [INSPIRE].
V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [hep-th/0402207] [INSPIRE].
N. Dorey and B. Vicedo, On the dynamics of finite-gap solutions in classical string theory, JHEP 07 (2006) 014 [hep-th/0601194] [INSPIRE].
B. Eynard, A short overview of the “Topological recursion”, arXiv:1412.3286 [INSPIRE].
B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion, Commun. Num. Theor. Phys. 1 (2007) 347 [math-ph/0702045] [INSPIRE].
G. Sizov and S. Valatka, Algebraic Curve for a Cusped Wilson Line, JHEP 05 (2014) 149 [arXiv:1306.2527] [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].
N. Drukker, 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model, JHEP 09 (2006) 004 [hep-th/0605151] [INSPIRE].
T. Enari and A. Miwa, Semi-classical correlator for 1/4 BPS Wilson loop and chiral primary operator with large R-charge, Phys. Rev. D 86 (2012) 106004 [arXiv:1208.0821] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results, arXiv:1108.6194 [INSPIRE].
N.M. Temme, Large parameter cases of the Gauss hypergeometric function, J. Comput. Appl. Math. 153 (2003) 441.
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: 2110.13126
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
Giombi, S., Komatsu, S. & Offertaler, B. Large charges on the Wilson loop in \( \mathcal{N} \) = 4 SYM: matrix model and classical string. J. High Energ. Phys. 2022, 20 (2022). https://doi.org/10.1007/JHEP03(2022)020
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)020