Spectral Form Factors from EFTs and Hydrodynamics

Spectral form factors (SFFs) are an important diagnostic of level repulsion in chaotic systems. Level repulsion can be supressed (and the SFF enhanced) when the system posesses additional symmetries. We investigate how the SFF behaves when these symmetries are broken. We find a result that transitions between the symmetric and nonsymmetric results. We then specifically investigate hydrodynamic systems, which have approximate conservation laws at every point. Our results give rise to novel quantum field theories, as well as reproducing established results in the case of simple diffusion.