@article{59660db817fb4001ab6ce7551176ec38,

title = "Testing holography using lattice super-Yang-Mills theory on a 2-torus",

abstract = "We consider maximally supersymmetric SU(N) Yang-Mills theory in Euclidean signature compactified on a flat two-dimensional torus with antiperiodic ({"}thermal{"}) fermion boundary conditions imposed on one cycle. At large N, holography predicts that this theory describes certain black hole solutions in type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N=16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory-Laflamme transition.",

author = "Simon Catterall and Jha, {Raghav G.} and David Schaich and Toby Wiseman",

note = "Funding Information: We thank Krai Cheamsawat, Joel Giedt, Anosh Joseph and Jamie Hudspith for helpful conversations. R. G. J. and T. W. thank the organizers of the April 2017 “Quantum Gravity, String Theory and Holography” workshop at Kyoto University{\textquoteright}s Yukawa Institute for Theoretical Physics, where this work was first presented and benefited from interesting discussions. This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of High Energy Physics, under Awards No. DE-SC0008669 (D. S.) and DE-SC0009998 (S. C., R. G. J., D. S.). Numerical calculations were carried out on the HEP-TH cluster at the University of Colorado, on the DOE-funded USQCD facilities at Fermilab, and at the San Diego Computing Center through XSEDE supported by National Science Foundation Grant No. ACI-1053575. Funding Information: R.G.J. and T.W. thank the organizers of the April 2017 Quantum Gravity, String Theory and Holography workshop at Kyoto University's Yukawa Institute for Theoretical Physics, where this work was first presented and benefited from interesting discussions. This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of High Energy Physics, under Awards No.DE-SC0008669 (D.S.) and DE-SC0009998 (S.C., R.G.J., D.S.). Numerical calculations were carried out on the HEP-TH cluster at the University of Colorado, on the DOE-funded USQCD facilities at Fermilab, and at the San Diego Computing Center through XSEDE supported by National Science Foundation Grant No.ACI-1053575. Publisher Copyright: {\textcopyright} 2018 authors. Published by the American Physical Society.",

year = "2018",

month = apr,

day = "30",

doi = "10.1103/PhysRevD.97.086020",

language = "English (US)",

volume = "97",

journal = "Physical Review D",

issn = "2470-0010",

publisher = "American Physical Society",

number = "8",

}