No abstract

We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.

We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters. In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions. We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT. We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe.

No abstract

We construct three dimensional Chern-Simons-matter theories with gauge groups U (N ) ×U (N ) and SU (N ) ×SU (N ) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U (N ) × U (N ) theory at level k describes the low energy limit of N M2-branes probing a C 4 /Z k singularity. At large N the theory is then dual to M-theory on AdS 4 × S 7 /Z k . The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS 4 × CP 3 . For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU (2) × SU (2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.

We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field.The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2, R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large N quantum mechanics systems with emergent reparametrization symmetry.This article is largely based on talks given by Kitaev [1], which motivated us to work out the details of the ideas described there.

We explain how the string spectrum in flat space and pp-waves arises from the large N limit, at fixed g 2 Y M , of U(N) N = 4 super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams.We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.

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