Abstract
In this paper we use lattice simulation to study four dimensional \( \mathcal{N} \) = 4 super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size 124 and for ’t Hooft couplings up to λ = 40.0. Our lattice action is based on a discretization of the Marcus or GL twist of \( \mathcal{N} \) = 4 SYM and retains one exact supersymmetry for non-zero lattice spacing. We show that lattice theory exists in a single non-Abelian Coulomb phase for all ’t Hooft couplings. Furthermore the static potential we obtain from correlators of Polyakov lines is in good agreement with that obtained from holography — specifically the potential has a Coulombic form with a coefficent that varies as the square root of the ’t Hooft coupling.
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References
S. Catterall, D.B. Kaplan and M. Unsal, Exact lattice supersymmetry, Phys. Rept. 484 (2009) 71 [arXiv:0903.4881] [INSPIRE].
S. Catterall, From Twisted Supersymmetry to Orbifold Lattices, JHEP 01 (2008) 048 [arXiv:0712.2532] [INSPIRE].
A.G. Cohen, D.B. Kaplan, E. Katz and M. Unsal, Supersymmetry on a Euclidean space-time lattice. 1. A Target theory with four supercharges, JHEP 08 (2003) 024 [hep-lat/0302017] [INSPIRE].
A.G. Cohen, D.B. Kaplan, E. Katz and M. Unsal, Supersymmetry on a Euclidean space-time lattice. 2. Target theories with eight supercharges, JHEP 12 (2003) 031 [hep-lat/0307012] [INSPIRE].
D.B. Kaplan and M. Unsal, A Euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP 09 (2005) 042 [hep-lat/0503039] [INSPIRE].
M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite N, Phys. Rev. D 94 (2016) 086010 [arXiv:1603.00538] [INSPIRE].
K.N. Anagnostopoulos, M. Hanada, J. Nishimura and S. Takeuchi, Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature, Phys. Rev. Lett. 100 (2008) 021601 [arXiv:0707.4454] [INSPIRE].
M. Hanada, A. Miwa, J. Nishimura and S. Takeuchi, Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics, Phys. Rev. Lett. 102 (2009) 181602 [arXiv:0811.2081] [INSPIRE].
S. Catterall and T. Wiseman, Black hole thermodynamics from simulations of lattice Yang-Mills theory, Phys. Rev. D 78 (2008) 041502 [arXiv:0803.4273] [INSPIRE].
S. Catterall and T. Wiseman, Extracting black hole physics from the lattice, JHEP 04 (2010) 077 [arXiv:0909.4947] [INSPIRE].
S. Catterall, A. Joseph and T. Wiseman, Thermal phases of D1-branes on a circle from lattice super Yang-Mills, JHEP 12 (2010) 022 [arXiv:1008.4964] [INSPIRE].
E. Berkowitz et al., Precision lattice test of the gauge/gravity duality at large-N, Phys. Rev. D 94 (2016) 094501 [arXiv:1606.04951] [INSPIRE].
S. Catterall, R.G. Jha, D. Schaich and T. Wiseman, Testing holography using lattice super-Yang-Mills theory on a 2-torus, Phys. Rev. D 97 (2018) 086020 [arXiv:1709.07025] [INSPIRE].
E. Rinaldi et al., Toward Holographic Reconstruction of Bulk Geometry from Lattice Simulations, JHEP 02 (2018) 042 [arXiv:1709.01932] [INSPIRE].
S. Catterall et al., Three-dimensional super-Yang-Mills theory on the lattice and dual black branes, Phys. Rev. D 102 (2020) 106009 [arXiv:2010.00026] [INSPIRE].
S. Catterall et al., Phase Structure of Lattice N = 4 Super Yang-Mills, JHEP 11 (2012) 072 [arXiv:1209.5285] [INSPIRE].
S. Catterall et al., N=4 Supersymmetry on a Space-Time Lattice, Phys. Rev. D 90 (2014) 065013 [arXiv:1405.0644] [INSPIRE].
S. Catterall, J. Giedt and G.C. Toga, Lattice \( \mathcal{N} \) = 4 super Yang-Mills at strong coupling, JHEP 12 (2020) 140 [arXiv:2009.07334] [INSPIRE].
S. Catterall and D. Schaich, Lifting flat directions in lattice supersymmetry, JHEP 07 (2015) 057 [arXiv:1505.03135] [INSPIRE].
N. Marcus, The Other topological twisting of N = 4 Yang-Mills, Nucl. Phys. B 452 (1995) 331 [hep-th/9506002] [INSPIRE].
A. Kapustin and E. Witten, Electric-Magnetic Duality And The Geometric Langlands Program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
S. Catterall, J. Giedt and A. Joseph, Twisted supersymmetries in lattice \( \mathcal{N} \) = 4 super Yang-Mills theory, JHEP 10 (2013) 166 [arXiv:1306.3891] [INSPIRE].
M.A. Clark, The Rational Hybrid Monte Carlo Algorithm, PoS LAT2006 (2006) 004 [hep-lat/0610048] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [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].
APE collaboration, Glueball Masses and String Tension in Lattice QCD, Phys. Lett. B 192 (1987) 163 [INSPIRE].
S.-X. Chu, D. Hou and H.-C. Ren, The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a N=4 Super Yang-Mills Vacuum, JHEP 08 (2009) 004 [arXiv:0905.1874] [INSPIRE].
Acknowledgments
This work was supported by the US Department of Energy (DOE), Office of Science, Office of High Energy Physics, under Award Numbers DE-SC0009998 (SC,GT) and DESC0013496 (JG). Numerical calculations were carried out on the DOE-funded USQCD facilities at Fermilab and NSF-funded ACCESS SDSC-Expanse facilities under Award number PHY170035.
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Catterall, S., Giedt, J. & Toga, G.C. Holography from lattice \( \mathcal{N} \) = 4 super Yang-Mills. J. High Energ. Phys. 2023, 84 (2023). https://doi.org/10.1007/JHEP08(2023)084
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DOI: https://doi.org/10.1007/JHEP08(2023)084