Schwinger-Keldysh hydrodynamics of the SYK lattice

Seminar series

String Theory Seminar

Date

Tue, 28 Apr 2026
13:00

Location

Speaker

Akash Jain

Organisation

Oxford

Hydrodynamics provides a universal low-energy effective description of interacting many-body systems. Traditionally, it is formulated in terms of equations of motion derived from the relevant conservation laws. However, this classical framework neglects fluctuations of hydrodynamic observables required by the fluctuation–dissipation theorem (FDT). The Schwinger–Keldysh effective field theory (SK EFT) offers a Wilsonian, action-based formulation of hydrodynamics that systematically incorporates such fluctuations. In this approach, the effective action is generically non-unitary (complex), encoding macroscopic dissipation, while the FDT is implemented through a discrete Kubo–Martin–Schwinger (KMS) symmetry. This symmetry also underlies the emergence of the second law of thermodynamics within hydrodynamics.

In this talk, we will discuss the first-ever derivation of an SK EFT directly from a local, unitary microscopic Hamiltonian. Specifically, we will consider a one-dimensional chain of SYK dots with Gaussian-random interactions between nearest neighbours. This system possesses a single conserved quantity—energy—and accordingly its low-energy dynamics are governed by an SK EFT for energy diffusion. We will identify the fundamental and emergent symmetries of this theory and derive the associated classical entropy current for SYK chains. Time permitting, we will also comment on applications to out-of-time-ordered correlators of energy fluctuations. The talk will be based on the recent paper with Marta, Mark, and Alexey: https://arxiv.org/pdf/2604.18675.