Abstract
The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group U(N ) are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from the representation theory of the symmetric group. This provides a proof of a recent observation by Okuyama. As a by-product, we present a new calculation of the connected 2-point correlator of multiplywound Wilson loops at leading order in 1/N.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313 (2012) 71 [arXiv:0712.2824] [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].
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].
G. Akemann and P.H. Damgaard, Wilson loops in N = 4 supersymmetric Yang-Mills theory from random matrix theory, Phys. Lett.B 513 (2001) 179 [Erratum ibid. B 524 (2002) 400] [hep-th/0101225] [INSPIRE].
S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP08 (2006) 026 [hep-th/0605027] [INSPIRE].
S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP05 (2006) 037 [hep-th/0603208] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson loops, JHEP08 (2006) 074 [hep-th/0604007] [INSPIRE].
K. Okuyama and G.W. Semenoff, Wilson loops in N = 4 SYM and fermion droplets, JHEP06 (2006) 057 [hep-th/0604209] [INSPIRE].
S. Yamaguchi, Bubbling geometries for half BPS Wilson lines, Int. J. Mod. Phys.A 22 (2007) 1353 [hep-th/0601089] [INSPIRE].
O. Lunin, On gravitational description of Wilson lines, JHEP06 (2006) 026 [hep-th/0604133] [INSPIRE].
B. Fiol and G. Torrents, Exact results for Wilson loops in arbitrary representations, JHEP01 (2014) 020 [arXiv:1311.2058] [INSPIRE].
J. Gordon, Antisymmetric Wilson loops in \( \mathcal{N} \)= 4 SYM beyond the planar limit, JHEP01 (2018) 107 [arXiv:1708.05778] [INSPIRE].
K. Okuyama, Connected correlator of 1/2 BPS Wilson loops in \( \mathcal{N} \)= 4 SYM, JHEP10 (2018) 037 [arXiv:1808.10161] [INSPIRE].
J. Ambjørn, L. Chekhov, C.F. Kristjansen and Yu. Makeenko, Matrix model calculations beyond the spherical limit, Nucl. Phys.B 404 (1993) 127 [Erratum ibid. B 449 (1995) 681] [hep-th/9302014] [INSPIRE].
X. Chen-Lin, Symmetric Wilson loops beyond leading order, SciPost Phys.1 (2016) 013 [arXiv:1610.02914] [INSPIRE].
A.F. Canazas Garay, A. Faraggi and W. Mück, Antisymmetric Wilson loops in \( \mathcal{N} \)= 4 SYM: from exact results to non-planar corrections, JHEP08 (2018) 149 [arXiv:1807.04052] [INSPIRE].
S. Förste, D. Ghoshal and S. Theisen, Stringy corrections to the Wilson loop in N = 4 superYang-Mills theory, JHEP08 (1999) 013 [hep-th/9903042] [INSPIRE].
N. Drukker, D.J. Gross and A.A. Tseytlin, Green-Schwarz string in AdS 5× S 5: semiclassical partition function, JHEP04 (2000) 021 [hep-th/0001204] [INSPIRE].
M. Kruczenski and A. Tirziu, Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling, JHEP05 (2008) 064 [arXiv:0803.0315] [INSPIRE].
A. Faraggi and L.A. Pando Zayas, The spectrum of excitations of holographic Wilson loops, JHEP05 (2011) 018 [arXiv:1101.5145] [INSPIRE].
A. Faraggi, W. Mück and L.A. Pando Zayas, One-loop effective action of the holographic antisymmetric Wilson loop, Phys. Rev.D 85 (2012) 106015 [arXiv:1112.5028] [INSPIRE].
A. Faraggi, J.T. Liu, L.A. Pando Zayas and G. Zhang, One-loop structure of higher rank Wilson loops in AdS/CFT, Phys. Lett.B 740 (2015) 218 [arXiv:1409.3187] [INSPIRE].
V. Forini et al., Precision calculation of 1/4-BPS Wilson loops in AdS 5 × S 5, JHEP02 (2016) 105 [arXiv:1512.00841] [INSPIRE].
A. Faraggi, L.A. Pando Zayas, G.A. Silva and D. Trancanelli, Toward precision holography with supersymmetric Wilson loops, JHEP04 (2016) 053 [arXiv:1601.04708] [INSPIRE].
M. Horikoshi and K. Okuyama, α′-expansion of anti-symmetric Wilson loops in \( \mathcal{N} \)= 4 SYM from Fermi gas, PTEP2016 (2016) 113B05 [arXiv:1607.01498] [INSPIRE].
V. Forini, A.A. Tseytlin and E. Vescovi, Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS 5× S 5, JHEP03 (2017) 003 [arXiv:1702.02164] [INSPIRE].
J. Aguilera-Damia et al., Toward precision holography in Type IIA with Wilson loops, JHEP08 (2018) 044 [arXiv:1805.00859] [INSPIRE].
J. Aguilera-Damia et al., Zeta-function regularization of holographic Wilson loops, Phys. Rev.D 98 (2018) 046011 [arXiv:1802.03016] [INSPIRE].
B. Fiol, J. Martínez-Montoya and A. Rios Fukelman, Wilson loops in terms of color invariants, JHEP05 (2019) 202 [arXiv:1812.06890] [INSPIRE].
D.J. Gross and W. Taylor, Twists and Wilson loops in the string theory of two-dimensional QCD, Nucl. Phys.B 403 (1993) 395 [hep-th/9303046] [INSPIRE].
D.J. Gross and H. Ooguri, Aspects of large N gauge theory dynamics as seen by string theory, Phys. Rev.D 58 (1998) 106002 [hep-th/9805129] [INSPIRE].
NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.22 (2019).
B.E. Sagan, The symmetric group, Springer, Germany (2001).
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1906.03816
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Canazas Garay, A.F., Faraggi, A. & Mück, W. Note on generating functions and connected correlators of 1/2-BPS Wilson loops in \( \mathcal{N} \) = 4 SYM theory. J. High Energ. Phys. 2019, 149 (2019). https://doi.org/10.1007/JHEP08(2019)149
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2019)149