Abstract
A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice \( \mathcal{N} \) =4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice structure, both the symmetries and the geometric interpretation of the fields. In this brief article we provide an explicit example of such a blocking scheme and illustrate its practicality in the context of a small scale Monte Carlo renormalization group calculation. We also discuss the implications of this result, and the possible ways in which to use it in order to obtain further information about the long distance theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.B. Kaplan and M. Ünsal, A Euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP 09 (2005) 042 [hep-lat/0503039] [INSPIRE].
S. Catterall, From Twisted Supersymmetry to Orbifold Lattices, JHEP 01 (2008) 048 [arXiv:0712.2532] [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, J. Giedt and A. Joseph, Twisted supersymmetries in lattice \( \mathcal{N} \) =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].
T. Ishii, G. Ishiki, S. Shimasaki and A. Tsuchiya, N = 4 Super Yang-Mills from the Plane Wave Matrix Model, Phys. Rev. D 78 (2008) 106001 [arXiv:0807.2352] [INSPIRE].
G. Ishiki, S.-W. Kim, J. Nishimura and A. Tsuchiya, Deconfinement phase transition in N =4 super Yang-Mills theory on R × S 3 from supersymmetric matrix quantum mechanics, Phys. Rev. Lett. 102 (2009) 111601 [arXiv:0810.2884] [INSPIRE].
G. Ishiki, S.-W. Kim, J. Nishimura and A. Tsuchiya, Testing a novel large-N reduction for N =4 super Yang-Mills theory on R × S 3, JHEP 09 (2009) 029 [arXiv:0907.1488] [INSPIRE].
M. Hanada, S. Matsuura and F. Sugino, Two-dimensional lattice for four-dimensional N =4 supersymmetric Yang-Mills, Prog. Theor. Phys. 126 (2011) 597 [arXiv:1004.5513] [INSPIRE].
M. Honda, G. Ishiki, J. Nishimura and A. Tsuchiya, Testing the AdS/CFT correspondence by Monte Carlo calculation of BPS and non-BPS Wilson loops in 4d N =4 super-Yang-Mills theory, PoS(LATTICE 2011)244 [arXiv:1112.4274] [INSPIRE].
M. Honda, G. Ishiki, S.-W. Kim, J. Nishimura and A. Tsuchiya, Direct test of the AdS/CFT correspondence by Monte Carlo studies of N =4 super Yang-Mills theory, JHEP 11 (2013) 200 [arXiv:1308.3525] [INSPIRE].
M. Ünsal, Twisted supersymmetric gauge theories and orbifold lattices, JHEP 10 (2006) 089 [hep-th/0603046] [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].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1408.7067
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Catterall, S., Giedt, J. Real space renormalization group for twisted lattice \( \mathcal{N} \) =4 super Yang-Mills. J. High Energ. Phys. 2014, 50 (2014). https://doi.org/10.1007/JHEP11(2014)050
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2014)050