Stephen Shenker

M theory as a matrix model: A Conjecture

We suggest and motivate a precise equivalence between uncompactified 11-dimensional M theory and the N={infinity} 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. {copyright} {ital 1997} {ital The American Physical Society}

Conformal invariance, supersymmetry and string theory

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.

The Conformal Field Theory of Orbifolds

A prescription for the calculation of any correlation function in orbifold conformal field theory is given. The method is applied to the scattering of four twisted string states, which allows the extraction of operator product coefficients of conformal twist fields. We derive Yukawa couplings in the effective field theory for fermionic strings on orbifolds.

Viscosity bound violation in higher derivative gravity

Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. After field redefinitions these theories reduce to Gauss-Bonnet gravity, which has special properties that allow us to compute the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.

A bound on chaos

A bstractWe 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 λL ≤ 2πkBT/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

The Analytic Geometry of Two-Dimensional Conformal Field Theory

Abstract Two-dimensional conformal field theory is formulated as analytic geometry on the universal moduli space of Riemann surfaces.

Viscosity bound and causality violation.

In recent work we showed that, for a class of conformal field theories (CFT) with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, eta/s, could violate the conjectured Kovtun-Starinets-Son viscosity bound, eta/s > or = 1/4 pi. In this Letter we argue, in the context of the same model, that tuning eta/s below (16/25)(1/4 pi) induces microcausality violation in the CFT, rendering the theory inconsistent. This is a concrete example in which inconsistency of a theory and a lower bound on viscosity are correlated, supporting the idea of a possible universal lower bound on eta/s for all consistent theories.

Black holes and the butterfly effect

A bstractWe 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.

Superconformal Invariance in Two-Dimensions and the Tricritical Ising Model

Abstract We discuss the realization of superconformal invariance in two dimensional quantum field theory. The Hilbert space of a superconformal theory splits into two sectors; one a representation of the Neveu-Schwarz algebra, the other of the Ramond algebra. We introduce the spin fields which intertwine the two sectors and correspond to the irreducible representations of the Ramond algebra. We give the determinant formula for the Ramond algebra and the discrete list of possible unitary representations. We have previously noted that the Z2 even sector of the tricritical Ising model is a representation of the Neveu-Schwarz algebra. Here we complete the picture by showing that the Z2 odd sector forms a representation of the Ramond algebra. This system is the first experimentally realizable supersymmetric field theory.

Covariant Quantization of Superstrings

Abstract We present a manifestly Lorentz covariant formulation of supersymmetric string theory. In particular, we construct the fermion vertex and the supersymmetry generators in a BRST quantization using the techniques of superconformal field theory.