Abstract
In this paper we present results from numerical simulations of \( \mathcal{N} \) = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action [1]. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Catterall, D.B. Kaplan and M. Ünsal, Exact lattice supersymmetry, Phys. Rept. 484 (2009) 71 [arXiv:0903.4881] [INSPIRE].
S. Catterall, E. Dzienkowski, J. Giedt, A. Joseph and R. Wells, Perturbative renormalization of lattice N = 4 super Yang-Mills theory, JHEP 04 (2011) 074 [arXiv:1102.1725] [INSPIRE].
S. Catterall, P.H. Damgaard, T. Degrand, R. Galvez and D. Mehta, Phase structure of lattice N = 4 super Yang-Mills, JHEP 11 (2012) 072 [arXiv:1209.5285] [INSPIRE].
S. Catterall, J. Giedt and A. Joseph, Twisted supersymmetries in lattice N = 4 super Yang-Mills theory, JHEP 10 (2013) 166 [arXiv:1306.3891] [INSPIRE].
S. Catterall, D. Schaich, P.H. Damgaard, T. DeGrand and J. Giedt, N = 4 supersymmetry on a space-time lattice, Phys. Rev. D 90 (2014) 065013 [arXiv:1405.0644] [INSPIRE].
D. Schaich, Progress and prospects of lattice supersymmetry, PoS(LATTICE2018)005 (2019) [arXiv:1810.09282] [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].
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].
E. Berkowitz, E. Rinaldi, M. Hanada, G. Ishiki, S. Shimasaki and P. Vranas, 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, E. Berkowitz, M. Hanada, J. Maltz and P. Vranas, Toward holographic reconstruction of bulk geometry from lattice simulations, JHEP 02 (2018) 042 [arXiv:1709.01932] [INSPIRE].
S. Catterall, J. Giedt, D. Schaich, P.H. Damgaard and T. DeGrand, Results from lattice simulations of N = 4 supersymmetric Yang-Mills, PoS(LATTICE2014)267 (2014) [arXiv:1411.0166] [INSPIRE].
S. Catterall and D. Schaich, Lifting flat directions in lattice supersymmetry, JHEP 07 (2015) 057 [arXiv:1505.03135] [INSPIRE].
W. Krauth, H. Nicolai and M. Staudacher, Monte Carlo approach to M-theory, Phys. Lett. B 431 (1998) 31 [hep-th/9803117] [INSPIRE].
T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large N gauge theory, Phys. Rev. Lett. 48 (1982) 1063 [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].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2009.07334
Rights and permissions
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.
About this article
Cite this article
Catterall, S., Giedt, J. & Toga, G.C. Lattice \( \mathcal{N} \) = 4 super Yang-Mills at strong coupling. J. High Energ. Phys. 2020, 140 (2020). https://doi.org/10.1007/JHEP12(2020)140
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2020)140