Abstract
We study the ’t Hooft expansion of d = 4 \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM) theory with the gauge group SO(N) or Sp(N). We consider the 1/N5 expansion with fixed gsN5, where gs denotes the string coupling of bulk type IIB string theory on AdS5 × \( \mathbbm{RP} \)5 and N5 refers to the RR 5-form flux through \( \mathbbm{RP} \)5. N5 differs from N due to a shift coming from the RR charge of O3-plane. As an example, we consider the 1/N5 expansion of the free energy of \( \mathcal{N} \) = 4 SYM on S4 and the 1/2 BPS circular Wilson loops in the fundamental representation of SO(N) or Sp(N). We find that the 1/N5 expansion is more “closed string like” than the ordinary 1/N expansion.
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References
E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].
B. Fiol, B. Garolera and G. Torrents, Exact probes of orientifolds, JHEP 09 (2014) 169 [arXiv:1406.5129] [INSPIRE].
S. Giombi and B. Offertaler, Wilson loops in N = 4 SO(N) SYM and D-branes in AdS5 × RP5, JHEP 10 (2021) 016 [arXiv:2006.10852] [INSPIRE].
L.F. Alday, S.M. Chester and T. Hansen, Modular invariant holographic correlators for N = 4 SYM with general gauge group, JHEP 12 (2021) 159 [arXiv:2110.13106] [INSPIRE].
D. Dorigoni, M.B. Green and C. Wen, Exact results for duality-covariant integrated correlators in N = 4 SYM with general classical gauge groups, arXiv:2202.05784 [INSPIRE].
M. Blau, K.S. Narain and E. Gava, On subleading contributions to the AdS/CFT trace anomaly, JHEP 09 (1999) 018 [hep-th/9904179] [INSPIRE].
O. Aharony and A. Rajaraman, String theory duals for mass deformed SO(N) and USp(2N) N = 4 SYM theories, Phys. Rev. D 62 (2000) 106002 [hep-th/0004151] [INSPIRE].
O. Bergman, E.G. Gimon and S. Sugimoto, Orientifolds, RR torsion, and k-theory, JHEP 05 (2001) 047 [hep-th/0103183] [INSPIRE].
R.L. Mkrtchian, The equivalence of Sp(2N) and SO(−2N) gauge theories, Phys. Lett. B 105 (1981) 174 [INSPIRE].
P. Cvitanovic and A.D. Kennedy, Spinors in negative dimensions, Phys. Scripta 26 (1982) 5 [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].
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. Zyczkowski and H.-J. Sommers, Hilbert-Schmidt volume of the set of mixed quantum states, J. Phys. A 36 (2003) 10115 [quant-ph/0302197].
I.G. Macdonald, The volume of a compact Lie group, Invent. Math. 56 (1980) 93.
H. Ooguri and C. Vafa, World sheet derivation of a large N duality, Nucl. Phys. B 641 (2002) 3 [hep-th/0205297] [INSPIRE].
I. Goulden, J. Harer and D. Jackson, A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves, Trans. Amer. Math. Soc. 353 (2001) 4405.
S. Sinha and C. Vafa, SO and Sp Chern-Simons at large N, hep-th/0012136 [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].
K. Okuyama, ’t Hooft expansion of 1/2 BPS Wilson loop, JHEP 09 (2006) 007 [hep-th/0607131] [INSPIRE].
K. Okuyama, Spectral form factor and semi-circle law in the time direction, JHEP 02 (2019) 161 [arXiv:1811.09988] [INSPIRE].
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Okuyama, K. ’t Hooft expansion of SO(N) and Sp(N) \( \mathcal{N} \) = 4 SYM revisited. J. High Energ. Phys. 2022, 64 (2022). https://doi.org/10.1007/JHEP09(2022)064
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DOI: https://doi.org/10.1007/JHEP09(2022)064