Phase transition of anti-symmetric Wilson loops in N=4 SYM

[1] 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].

[2] 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].

[3] V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,

Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].

[4] J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859

[hep-th/9803002] [INSPIRE].

[5] 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].

[6] N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02

(2005) 010 [hep-th/0501109] [INSPIRE].

[7] S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05

(2006) 037 [hep-th/0603208] [INSPIRE].

– 21 –

JHEP12(2017)125

It would be interesting find the closed form expression of the higher order terms in a.

From (4.1), WAk with fixed k can also be computed once we know the generating

function J(z). At the leading order in 1/N , the integral (4.1) is evaluated by the saddle

point approximation, and the leading term S0 is just given by the Legendre transformation

of J0 (z) (4.3). From the small λ expansion of J0 (z) in (2.10) we can easily find the small

λ expansion of the solution z∗ of the saddle point equation (4.4)

[8] S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08

(2006) 026 [hep-th/0605027] [INSPIRE].

[9] K. Okuyama and G.W. Semenoff, Wilson loops in N = 4 SYM and fermion droplets, JHEP

06 (2006) 057 [hep-th/0604209] [INSPIRE].

[10] J. Gomis and F. Passerini, Holographic Wilson Loops, JHEP 08 (2006) 074

[hep-th/0604007] [INSPIRE].

[11] J. Gomis and F. Passerini, Wilson Loops as D3-branes, JHEP 01 (2007) 097

[hep-th/0612022] [INSPIRE].

[13] 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].

[14] 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].

[15] A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops,

JHEP 05 (2011) 018 [arXiv:1101.5145] [INSPIRE].

[16] K. Zarembo, Localization and AdS/CFT Correspondence, J. Phys. A 50 (2017) 443011

[arXiv:1608.02963] [INSPIRE].

[17] X. Chen-Lin, Symmetric Wilson Loops beyond leading order, SciPost Phys. 1 (2016) 013

[arXiv:1610.02914] [INSPIRE].

[18] J. Gordon, Antisymmetric Wilson loops in N = 4 SYM beyond the planar limit,

arXiv:1708.05778 [INSPIRE].

[19] B. Fiol and G. Torrents, Exact results for Wilson loops in arbitrary representations, JHEP

01 (2014) 020 [arXiv:1311.2058] [INSPIRE].

[20] U. Haagerup and S. Thorbjørnsen, Asymptotic expansions for the Gaussian Unitary

Ensemble, arXiv:1004.3479.

[21] B. Eynard, Topological expansion for the 1-Hermitian matrix model correlation functions,

JHEP 11 (2004) 031 [hep-th/0407261] [INSPIRE].

[22] B. Eynard and N. Orantin, Algebraic methods in random matrices and enumerative

geometry, arXiv:0811.3531 [INSPIRE].

[23] M. Horikoshi and K. Okuyama, α0 -expansion of Anti-Symmetric Wilson Loops in N = 4

SYM from Fermi Gas, Prog. Theor. Exp. Phys. 2016 (2016) 113B05 [arXiv:1607.01498]

[INSPIRE].

[24] A.A. Migdal, Loop Equations and 1/N Expansion, Phys. Rept. 102 (1983) 199 [INSPIRE].

[25] T. Morita and K. Sugiyama, Multi-cut Solutions in Chern-Simons Matrix Models,

arXiv:1704.08675 [INSPIRE].

[26] S. Yamaguchi, Bubbling geometries for half BPS Wilson lines, Int. J. Mod. Phys. A 22

(2007) 1353 [hep-th/0601089] [INSPIRE].

[27] O. Lunin, On gravitational description of Wilson lines, JHEP 06 (2006) 026

[hep-th/0604133] [INSPIRE].

– 22 –

JHEP12(2017)125

[12] 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].

[28] E. D’Hoker, J. Estes and M. Gutperle, Gravity duals of half-BPS Wilson loops, JHEP 06

(2007) 063 [arXiv:0705.1004] [INSPIRE].

[29] T. Okuda and D. Trancanelli, Spectral curves, emergent geometry and bubbling solutions for

Wilson loops, JHEP 09 (2008) 050 [arXiv:0806.4191] [INSPIRE].

[30] J. Aguilera-Damia, D.H. Correa, F. Fucito, V.I. Giraldo-Rivera, J.F. Morales and

L.A. Pando Zayas, Strings in Bubbling Geometries and Dual Wilson Loop Correlators,

arXiv:1709.03569 [INSPIRE].

[31] E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories,

Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

JHEP12(2017)125

– 23 –

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