For a weakly nonlinear classical system, the kinetic equation for waves governs the evolution of the occupation number of a given wavevector. It is like the Boltzmann equation, but for waves instead of particles. As has been known for half a century, in addition to thermal equilibrium, the kinetic equation has another stationary solution: a turbulent state, describing a cascade of energy. Wave turbulence is observed in a wide range of physical contexts, most notably in surface gravity waves in the ocean. Higher order terms in the kinetic equation, going beyond leading order in the nonlinearity, have never been computed. We describe a method, based on quantum field theory, for computing such terms. We show that higher order terms can exhibit UV divergences. We sum the most divergent diagrams (bubble diagrams) to derive a kind of renormalized kinetic equation. Based on 2203.08168, 2212.02555, and work in progress with G. Falkovich. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

The n-point tachyon amplitude is a classic and well-known result in bosonic string theory. Rather than studying tachyon amplitudes, we will compute scattering amplitudes involving highly excited string states. Along the way we review and elaborate on the DDF construction of string vertex operators, and describe properties of a generic excited string. Based on work in progress with D. Gross.

Most recent discussions of holography in AdS_2/CFT_1 have focused on the Schwarzian and JT gravity. However, the AdS dual of SYK is expected to, in addition, contain an infinite tower of massive fields. The interactions for these fields are in principle fixed by the SYK correlation functions. We review the construction of all-point correlation functions in SYK. We comment on the difficulties in finding a coherent description of the bulk tower of fields. Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting.

The SYK model, and more generally, tensor models, are a new class of large N quantum field theories. We discuss the computation of all-point correlation functions in the SYK model, at leading order in 1/N. The result has remarkable simplicity and structure. The result is general, holding for any theory in which one forms higher-point correlators by gluing together four-point functions; for instance, large N vector models and tensor models. It implies specific singularity structure of analytically extended OPE coefficients. In particular, the analytically extended OPE coefficients of the single-trace operators encode the OPE coefficients of the double-trace operators.

We discuss the computation of all-point correlation functions in the SYK model, at leading order in 1/N. The result has remarkable simplicity and structure. The result is general, holding for any theory in which one forms higher-point correlators by gluing together four-point functions; for instance, large N vector models and tensor models. It implies specific singularity structure of analytically extended OPE coefficients. In particular, the analytically extended OPE coefficients of the single-trace operators encode the OPE coefficients of the double-trace operators