We consider the problem of how fast a quantum system can scramble (thermalize) information, given that the interactions are between bounded clusters of degrees of freedom; pairwise interactions would be an example. Based on previous work, we conjecture:1) The most rapid scramblers take a time logarithmic in the number of degrees of freedom.2)Matrix quantum mechanics (systems whose degrees of freedom are n by n matrices) saturate the bound.3) Black holes are the fastest scramblers in nature.The conjectures are based on two sources, one from quantum information theory, and the other from the study of black holes in String Theory.

In this paper we provide some circumstantial evidence for a holographic duality between bubble nucleation in an eternally inflating universe and a Euclidean conformal field theory. The holographic correspondence (which is different than Strominger's dS/CFT duality) relates the decay of (3+1)-dimensional de Sitter space to a two-dimensional CFT. It is not associated with pure de Sitter space, but rather with Coleman-De Luccia bubble nucleation. Alternatively, it can be thought of as a holographic description of the open, infinite, FRW cosmology that results from such a bubble.The conjectured holographic representation is of a new type that combines holography with the Wheeler-DeWitt formalism to produce a Wheeler-DeWitt theory that lives on the spatial boundary of a k = −1 FRW cosmology.We also argue for a more ambitious interpretation of the Wheeler-DeWitt CFT as a holographic dual of the entire Landscape.

Guided by the generalized conformal symmetry, we investigate the extension of AdS-CFT correspondence to the matrix model of D-particles in the large N limit. We perform a complete harmonic analysis of the bosonic linearized fluctuations around a heavy Dparticle background in IIA supergravity in 10 dimensions and find that the spectrum precisely agrees with that of the physical operators of Matrix theory. The explicit forms of two-point functions give predictions for the large N behavior of Matrix theory with some special cutoff. We discuss the possible implications of our results for the large N dynamics of D-particles and for the Matrix-theory conjecture. We find an anomalous scaling behavior with respect to the large N limit associated to the infinite momentum limit in 11 dimensions, suggesting the existence of a screening mechanism for the transverse extension of the system.

We develop a systematic method of directly embedding supermembrane wrapped around a circle into matrix string theory. Our purpose is to study connection between matrix string and membrane from an entirely 11 dimensional point of view. The method does neither rely upon the DLCQ limit nor upon string dualities. In principle, this enables us to construct matrix string theory with arbitrary backgrounds from the corresponding supermembrane theory. As a simplest application of the formalism, the matrix-string action with a 7 brane background (Kaluza-Klein Melvin solution) with nontrivial RR vector field is given.

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-

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 firstprinciple 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.

As an extension of the so-called BMN conjecture, we investigate the plane-wave limit for possible holographic connection between bulk string theories in non-conformal backgrounds of Dp-branes and the corresponding supersymmetric gauge theories for p < 5.Our work is based on the tunneling picture for dominant null trajectories of strings in the limit of large angular momentum. The tunneling null trajectories start from the near-horizon boundary and return to the boundary, and the resulting backgrounds are time-dependent for general Dp-branes except for p = 3. We develop a general method for extracting diagonalized two-point functions for boundary theories as Euclidean (bulk) S-matrix in the time-dependent backgrounds. For the case of D0-brane, two-point functions of supergravity modes are shown to agree with the results derived previously by the perturbative analysis of supergravity. We then discuss the implications of the holography for general cases of Dp-branes including the stringy excitations. All the cases (p = 3, p < 5) exhibit interesting infra-red behaviors, which are different from free-field theories, suggesting the existence of quite nontrivial fixed-points in dual gauge theories.

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p, q) fivebranes and (p, q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p, q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.