We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = ∞ limit of the supersymmetric matrix quantum mechanics describing D0 branes . The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity . The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.Comment: 16+6 pages, 2 figure

We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the $t = 0$ slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.Comment: 29 pages, 4 figures. v2: references added/clarified, typos corrected. v3: reference added, referencing clarifie

Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be used to study string compactification and dynamics.