Interaction Renormalization and Validity of Kinetic Equations for Turbulent States.

We consider turbulence of waves interacting weakly via four-wave scattering (sea waves, plasma waves, spin waves, etc.). In the first order in the interaction, a closed kinetic equation has stationary solutions describing turbulent cascades.

Wave turbulence and the kinetic equation beyond leading order.

We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method and is based on an analogy between the Liouville equation in infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: A broad class of nonlinear classical field theories are believed to have a stationary turbulent state-a far-from-equilibrium state, even at weak coupling.

Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model.

We point out that a classical analog of the Sachdev-Ye-Kitaev (SYK) model, a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equation in the turbulent regime and the nonlinear Schrödinger equation describing plasma turbulence, in which there is mixing between many different modes, the random coupling model has a Gaussian-random coupling between any four of a large number N of modes. The model was solved in the 1960s, before the introduction of large-N path-integral techniques, using a method referred to as the direct interaction approximation.

Chaos in a Many-String Scattering Amplitude.

String theory provides a compact integral expression for the tree-level scattering amplitude of an arbitrary number of light strings. We focus on amplitudes involving a few tachyons and many photons, with a special choice of polarizations and kinematics. We pick out a particular pole in the amplitude-one corresponding to successive photon scatterings, which lead to an intermediate state with a highly excited string in a definite state.

Chaos in the Quantum Field Theory S-Matrix.

A number of studies have shown that chaos occurs in scattering: the outgoing deflection angle is seen to be an erratic function of the impact parameter. We propose to extend this to quantum field theory and to use the erratic behavior of the many-particle S-matrix as a probe of chaos.

Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Corrections.

Recently, Almheiri, Dong, and Harlow have argued that the localization of bulk information in a boundary dual should be understood in terms of quantum error correction. We show that this structure appears naturally when the gauge invariance of the boundary theory is incorporated. This provides a new understanding of the nonuniqueness of the bulk fields (precursors).

Entanglement entropy flow and the Ward identity.

We derive differential equations for the flow of entanglement entropy as a function of the metric and the couplings of the theory. The variation of the universal part of entanglement entropy under a local Weyl transformation is related to the variation under a local change in the couplings. We show that this relation is, in fact, equivalent to the trace Ward identity.

A geometric solution to the coincidence problem, and the size of the landscape as the origin of hierarchy.

Weinberg's seminal prediction of the cosmological constant relied on a provisional method for regulating eternal inflation which has since been put aside. We show that a modern regulator, the causal patch, improves agreement with observation, removes many limiting assumptions, and yields additional powerful results. Without assuming necessary conditions for observers such as galaxies or entropy production, the causal patch measure predicts the coincidence of vacuum energy and present matter density.