Direct test of the gauge-gravity correspondence for Matrix theory correlation functions. (English) Zbl 1306.81107

Hanada, Masanori; Nishimura, Jun; Sekino, Yasuhiro; Yoneya, Tamiaki

J. High Energy Phys. 2011, No. 12, Paper No. 020, 44 p. (2011).

Summary: We study correlation functions in (0 + 1)-dimensional maximally supersym-metric U(\(N\)) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform first-principle calculations using Monte Carlo simulations, and compare the results against the predictions obtained previously based on the gauge-gravity correspondence from 10 dimensions. After providing a self-contained review on these predictions, we present clear evidence that the predictions in the large-\(N\) limit actually hold even at small \(N\) such as \(N =2\) and 3. The predicted behavior seems to continue to the far infrared regime, which goes beyond the naive range of validity of the 10D supergravity analysis. This suggests that the correlation functions also contain important information on the M-theory limit.

MSC:

81T13	Yang-Mills and other gauge theories in quantum field theory
81V17	Gravitational interaction in quantum theory
81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60	Supersymmetric field theories in quantum mechanics
83E50	Supergravity
83E15	Kaluza-Klein and other higher-dimensional theories
81T16	Nonperturbative methods of renormalization applied to problems in quantum field theory
65C05	Monte Carlo methods

Keywords:

gauge-gravity correspondence; M(atrix) theories; nonperturbative effects

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