We study correlation functions in ($0+1$)-dimensional maximally supersymmetric $\mathrm{U}(N)$ gauge theory, which represents the low-energy effective theory of D0-branes. In the large-$N$ limit, the gauge-gravity duality predicts power-law behaviors in the infrared region for the two-point correlation functions of operators corresponding to supergravity modes. We evaluate such correlation functions on the gauge theory side by the Monte Carlo method. Clear power-law behaviors are observed at $N=3$, and the predicted exponents are confirmed consistently. Our results suggest that the agreement extends to the $M$-theory regime, where the supergravity analysis in 10 dimensions may not be justified a priori.

• Received 25 January 2010

DOI:https://doi.org/10.1103/PhysRevLett.104.151601