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.
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