Abstract
We derive exact formulas for circular Wilson loops in the \( \mathcal{N} \) = 4 and \( \mathcal{N} \) = 2* theories with gauge groups U(N) and SU(N) in the k-fold symmetrized product representation. The formulas apply in the limit of large k and small Yang-Mills coupling g, with fixed effective coupling κ ≡ g2k, and for any finite N. In the SU(2) and U(2) cases, closed analytic formulas are obtained for any k, while the 1/k series expansions are asymptotic. In the N ≫ 1 limit, with N ≪ k, there is an overlapping regime where the formulas can be confronted with results from holography. Simple formulas for correlation functions between the k-symmetric Wilson loops and chiral primary operators are also given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.A. Gaumé, D. Orlando and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rept. 933 (2021) 1 [arXiv:2008.03308] [INSPIRE].
A. Bourget, D. Rodriguez-Gomez and J.G. Russo, A limit for large R-charge correlators in \( \mathcal{N} \) = 2 theories, JHEP 05 (2018) 074 [arXiv:1803.00580] [INSPIRE].
M. Beccaria, On the large R-charge \( \mathcal{N} \) = 2 chiral correlators and the Toda equation, JHEP 02 (2019) 009 [arXiv:1809.06280] [INSPIRE].
M. Beccaria, Double scaling limit of N = 2 chiral correlators with Maldacena-Wilson loop, JHEP 02 (2019) 095 [arXiv:1810.10483] [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].
A. Grassi, Z. Komargodski and L. Tizzano, Extremal correlators and random matrix theory, JHEP 04 (2021) 214 [arXiv:1908.10306] [INSPIRE].
D. Rodriguez-Gomez, A scaling limit for line and surface defects, JHEP 06 (2022) 071 [arXiv:2202.03471] [INSPIRE].
G. Cuomo, Z. Komargodski, M. Mezei and A. Raviv-Moshe, Spin impurities, Wilson lines and semiclassics, JHEP 06 (2022) 112 [arXiv:2202.00040] [INSPIRE].
G. Cuomo, Z. Komargodski and M. Mezei, Localized magnetic field in the O(N) model, JHEP 02 (2022) 134 [arXiv:2112.10634] [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].
C. Hoyos, A defect action for Wilson loops, JHEP 07 (2018) 045 [arXiv:1803.09809] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Wilson loop in general representation and RG flow in 1D defect QFT, J. Phys. A 55 (2022) 255401 [arXiv:2202.00028] [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 and A.A. Tseytlin, On non-supersymmetric generalizations of the Wilson-Maldacena loops in N = 4 SYM, Nucl. Phys. B 934 (2018) 466 [arXiv:1804.02179] [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].
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].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
M.L. Mehta, Random Matrices, Academic Press (1991).
K. Okuyama and G.W. Semenoff, Wilson loops in N = 4 SYM and fermion droplets, JHEP 06 (2006) 057 [hep-th/0604209] [INSPIRE].
S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [INSPIRE].
B. Fiol and G. Torrents, Exact results for Wilson loops in arbitrary representations, JHEP 01 (2014) 020 [arXiv:1311.2058] [INSPIRE].
X. Chen-Lin and K. Zarembo, Higher Rank Wilson Loops in N = 2* Super-Yang-Mills Theory, JHEP 03 (2015) 147 [arXiv:1502.01942] [INSPIRE].
B. Fiol, J. Martínez-Montoya and A. Rios Fukelman, Wilson loops in terms of color invariants, JHEP 05 (2019) 202 [arXiv:1812.06890] [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].
E.I. Buchbinder and A.A. Tseytlin, 1/N correction in the D3-brane description of a circular Wilson loop at strong coupling, Phys. Rev. D 89 (2014) 126008 [arXiv:1404.4952] [INSPIRE].
W. Mück, Combinatorics of Wilson loops in \( \mathcal{N} \) = 4 SYM theory, JHEP 11 (2019) 096 [arXiv:1908.11582] [INSPIRE].
F. Galvagno and M. Preti, Wilson loop correlators in \( \mathcal{N} \) = 2 superconformal quivers, JHEP 11 (2021) 023 [arXiv:2105.00257] [INSPIRE].
I. Aniceto, J.G. Russo and R. Schiappa, Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories, JHEP 03 (2015) 172 [arXiv:1410.5834] [INSPIRE].
E. Gerchkovitz, J. Gomis, N. Ishtiaque, A. Karasik, Z. Komargodski and S.S. Pufu, Correlation Functions of Coulomb Branch Operators, JHEP 01 (2017) 103 [arXiv:1602.05971] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Large N Correlation Functions in Superconformal Field Theories, JHEP 06 (2016) 109 [arXiv:1604.07416] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Operator mixing in large N superconformal field theories on S4 and correlators with Wilson loops, JHEP 12 (2016) 120 [arXiv:1607.07878] [INSPIRE].
M. Billó, F. Galvagno, P. Gregori and A. Lerda, Correlators between Wilson loop and chiral operators in \( \mathcal{N} \) = 2 conformal gauge theories, JHEP 03 (2018) 193 [arXiv:1802.09813] [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].
J.G. Russo and K. Zarembo, Evidence for Large-N Phase Transitions in N = 2* Theory, JHEP 04 (2013) 065 [arXiv:1302.6968] [INSPIRE].
J.G. Russo and K. Zarembo, Massive N = 2 Gauge Theories at Large N, JHEP 11 (2013) 130 [arXiv:1309.1004] [INSPIRE].
J.G. Russo, \( \mathcal{N} \) = 2 gauge theories and quantum phases, JHEP 12 (2014) 169 [arXiv:1411.2602] [INSPIRE].
T.J. Hollowood and S.P. Kumar, Partition function of \( \mathcal{N} \) = 2* SYM on a large four-sphere, JHEP 12 (2015) 016 [arXiv:1509.00716] [INSPIRE].
J.G. Russo, Large Nc from Seiberg-Witten Curve and Localization, Phys. Lett. B 748 (2015) 19 [arXiv:1504.02958] [INSPIRE].
J.G. Russo, Properties of the partition function of \( \mathcal{N} \) = 2 supersymmetric QCD with massive matter, JHEP 07 (2019) 125 [arXiv:1905.05267] [INSPIRE].
D.M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018) 005 [arXiv:1707.08577] [INSPIRE].
S. Hellerman, On the exponentially small corrections to \( \mathcal{N} \) = 2 superconformal correlators at large R-charge, arXiv:2103.09312 [INSPIRE].
M. Billó, M. Frau, F. Galvagno, A. Lerda and A. Pini, Strong-coupling results for \( \mathcal{N} \) = 2 superconformal quivers and holography, JHEP 10 (2021) 161 [arXiv:2109.00559] [INSPIRE].
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: 2206.09935
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
Rodriguez-Gomez, D., Russo, J.G. Wilson loops in large symmetric representations through a double-scaling limit. J. High Energ. Phys. 2022, 253 (2022). https://doi.org/10.1007/JHEP08(2022)253
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)253