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We argue that the space-time uncertainty relation of the form $\ensuremath{\Delta}X\ensuremath{\Delta}T\ensuremath{\gtrsim}{\ensuremath{\alpha}}^{\ensuremath{'}}$ for the observability of the distances with respect to time, $\ensuremath{\Delta}T$, and space, $\ensuremath{\Delta}X$, is universally valid in string theory including D-branes. This relation has been previously proposed by one (T. Y.) of the present authors as a simple qualitative representation of the perturbative short-distance structure of fundamental string theory. We show that the relation, combined with the usual quantum mechanical uncertainty principle, explains the key qualitative features of D-particle dynamics.

We study correlation functions in (0+1)-dimensional maximally supersymmetric 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., 4 pages, 3 figures