Direct test of the gauge-gravity correspondence for Matrix theory correlation functions

TL;DR

This paper provides a direct numerical test of the gauge-gravity correspondence in Matrix theory by comparing Monte Carlo simulation results of correlation functions with theoretical predictions, showing agreement even at small N.

Contribution

It offers the first-principles Monte Carlo verification of gauge-gravity predictions in (0+1)D maximally supersymmetric Yang-Mills theory, extending validity to small N and infrared regimes.

Findings

Predictions hold at small N (N=2,3)

Correlation functions match gauge-gravity predictions

Results suggest relevance to M-theory limit

Abstract

We study correlation functions in (0+1)-dimensional maximally supersymmetric 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.