Abstract
For \( \mathcal{N} \) = 2∗ theory with U(N ) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigen-value distributions in various regimes of parameters (N, λ, n, k) where λ is the ’t Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the \( \mathcal{N} \) = 4 limit of the \( \mathcal{N} \) = 2∗ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.
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References
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 and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [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].
S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].
S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [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].
K. Zarembo, Localization and AdS/CFT Correspondence, J. Phys. A 50 (2017) 443011 [arXiv:1608.02963] [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].
K. Zarembo, Strong-Coupling Phases of Planar N = 2* super-Yang-Mills Theory, Theor. Math. Phys. 181 (2014) 1522 [arXiv:1410.6114] [INSPIRE].
A. Buchel, J.G. Russo and K. Zarembo, Rigorous Test of Non-conformal Holography: Wilson Loops in N = 2* Theory, JHEP 03 (2013) 062 [arXiv:1301.1597] [INSPIRE].
N. Bobev, H. Elvang, D.Z. Freedman and S.S. Pufu, Holography for N = 2∗ on S 4, JHEP 07 (2014) 001 [arXiv:1311.1508] [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].
X. Chen-Lin, A. Dekel and K. Zarembo, Holographic Wilson loops in symmetric representations in \( \mathcal{N} \) = 2∗ super-Yang-Mills theory, JHEP 02 (2016) 109 [arXiv:1512.06420] [INSPIRE].
X. Chen-Lin, D. Medina-Rincon and K. Zarembo, Quantum String Test of Nonconformal Holography, JHEP 04 (2017) 095 [arXiv:1702.07954] [INSPIRE].
B. Eynard, T. Kimura and S. Ribault, Random matrices, arXiv:1510.04430 [INSPIRE].
T. Okuda, A Prediction for bubbling geometries, JHEP 01 (2008) 003 [arXiv:0708.3393] [INSPIRE].
N. Halmagyi and T. Okuda, Bubbling Calabi-Yau geometry from matrix models, JHEP 03 (2008) 028 [arXiv:0711.1870] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Gravity duals of half-BPS Wilson loops, JHEP 06 (2007) 063 [arXiv:0705.1004] [INSPIRE].
T. Okuda and D. Trancanelli, Spectral curves, emergent geometry and bubbling solutions for Wilson loops, JHEP 09 (2008) 050 [arXiv:0806.4191] [INSPIRE].
W. Fulton and J. Harris, Representation Theory: A First Course, Graduate Texts in Mathematics, Springer, New York U.S.A. (1991).
M. Lüscher, Symmetry Breaking Aspects of the Roughening Transition in Gauge Theories, Nucl. Phys. B 180 (1981) 317 [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].
A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops, JHEP 05 (2011) 018 [arXiv:1101.5145] [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].
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].
J. Cookmeyer, J.T. Liu and L.A. Pando Zayas, Higher Rank ABJM Wilson Loops from Matrix Models, JHEP 11 (2016) 121 [arXiv:1609.08165] [INSPIRE].
B. Eynard, Topological expansion for the 1-Hermitian matrix model correlation functions, JHEP 11 (2004) 031 [hep-th/0407261] [INSPIRE].
M. Horikoshi and K. Okuyama, α ′ -expansion of Anti-Symmetric Wilson Loops in \( \mathcal{N} \) = 4 SYM from Fermi Gas, PTEP 2016 (2016) 113B05 [arXiv:1607.01498] [INSPIRE].
X. Chen-Lin, Symmetric Wilson Loops beyond leading order, SciPost Phys. 1 (2016) 013 [arXiv:1610.02914] [INSPIRE].
J. Gordon, Antisymmetric Wilson loops in \( \mathcal{N} \) = 4 SYM beyond the planar limit, arXiv:1708.05778 [INSPIRE].
K. Okuyama, Phase Transition of Anti-Symmetric Wilson Loops in \( \mathcal{N} \) = 4 SYM, arXiv:1709.04166 [INSPIRE].
K. Pilch and N.P. Warner, N=2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].
A. Faraggi, W. Mueck 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].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons Theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [INSPIRE].
W. Mück, L.A. Pando Zayas and V. Rathee, Spectra of Certain Holographic ABJM Wilson Loops in Higher Rank Representations, JHEP 11 (2016) 113 [arXiv:1609.06930] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Wilson loops and chiral correlators on squashed spheres, JHEP 11 (2015) 064 [arXiv:1507.05426] [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].
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Liu, J.T., Zayas, L.A.P. & Zhou, S. Comments on higher rank Wilson loops in \( \mathcal{N} \) = 2∗. J. High Energ. Phys. 2018, 47 (2018). https://doi.org/10.1007/JHEP01(2018)047
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DOI: https://doi.org/10.1007/JHEP01(2018)047