Monte Carlo Studies of Matrix Theory Correlation Functions

Abstract

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.PACS numbers: 11.25.-w; 11.25.SqIntroduction.-Maximally supersymmetric YangMills theories (SYM) in various dimensions are important because of their connection to non-perturbative formulations of string theory. Of particular interest is the (0+1)D SYM with U (N ) gauge symmetry, which is supposed to describe the low-energy gravitational dynamics of D0-branes in 10D type IIA superstring theory. In an appropriate large-N limit, this theory was proposed to be a definition of M-theory in a special light-like frame, and it is commonly referred to as the Matrix theory [1]. M-theory is a hypothetical 11D theory [2], whose low energy effective theory is given by 11D supergravity, and it is believed to appear in the strong coupling limit of 10D type IIA superstring theory.Indeed it was confirmed that scattering amplitudes in the Matrix theory at weak coupling are consistent with predictions from 11D supergravity. Even the three-body force, which is a characteristic non-linear effect of general relativity, has been reproduced [3] from the quantum loop effects of massive open strings connecting D0-branes. On the other hand, direct perturbative calculations of correlation functions, which could provide crucial information on the as yet mysterious theory, are plagued by severe infrared divergences caused by the massless modes inherent in the theory. We therefore need genuinely nonperturbative methods to study such quantities.In the case of N =4 SYM in (3+1) dimensions, various useful insights have been gained from the AdS/CFT correspondence [4,5]. This conjectural duality enables us to study the N = 4 SYM in the large-N limit with large 't Hooft coupling constant by using the weakly coupled supergravity, which describes the low-energy limit of the string theory. Likewise, SYM in (p+1)-dimensions, corresponding to the world-volume theory of Dp-branes, is expected to be dual to a superstring theory on the Dp-

Covariantized matrix theory for D-particles

“…One thing among more recent works to be mentioned seems that we now have some suggestive results on non-perturbative properties using numerical simulations. For instance, we have reported results [8,9] about the correlation functions of super Yang-Mills quantum mechanics, which are consistent with the predictions [10] obtained from a "holographic" approach on the relation between 10D reduced 11D supergravity and super Yang-Mills quantum mechanics.…”

Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice

“…Several lattice formulations of SYM theories were proposed in and enabled us to perform direct tests of the duality. In one dimensional SYM with 16 supercharges, some evidences of the correspondence between the gauge theory and the dual black hole [34] have been obtained from numerical simulations [35][36][37][38][39][40][41][42][43]. In two-dimensional N = (8,8) SYM, lattice simulations have been already performed and the phase structure of the theory was investigated [44,45].…”

Precision lattice test of the gauge/gravity duality at large N

“…[11].) Previously, there have been attempts to study the internal energy [10,[12][13][14][15], the supersymmetric Polyakov loop [16] and two-point correlation functions [17,18].…”