Resurgence in Extended Hydrodynamics

TL;DR

This paper explores how the divergence and resurgence properties of hydrodynamic series are affected when the spectrum includes complex conjugate nonhydrodynamic modes, similar to black brane quasinormal modes in AdS/CFT.

Contribution

It extends the understanding of hydrodynamic series resurgence to cases with richer nonhydrodynamic mode spectra, specifically with complex conjugate modes.

Findings

Hydrodynamic series remains divergent and consistent with resurgence.

The series encodes information about nonhydrodynamic modes.

Complex conjugate modes influence the resurgence structure.

Abstract

It has recently been understood that the hydrodynamic series generated by the M\"uller-Israel-Stewart theory is divergent, and that this large order behaviour is consistent with the theory of resurgence. Furthermore, it was observed, that the physical origin of this is the presence of a purely damped nonhydrodynamic mode. It is very interesting to ask whether this picture persists in cases where the spectrum of nonhydrodynamic modes is richer. We take the first step in this direction by considering the simplest hydrodynamic theory which, instead of the purely damped mode, contains a pair of nonhydrodynamic modes of complex conjugate frequencies. This mimics the pattern of black brane quasinormal modes which appear on the gravity side of the AdS/CFT description of \symm\ plasma. We find that the resulting hydrodynamic series is divergent in a way consistent with resurgence and precisely encodes information about the nonhydrodynamic modes of the theory.