The large proper-time expansion of Yang-Mills plasma as a resurgent transseries

TL;DR

This paper demonstrates that the late-time energy density expansion of $ ext{N}=4$ supersymmetric Yang-Mills plasma can be expressed as a multi-parameter transseries, revealing nonhydrodynamic contributions and their recoverability through resurgence techniques.

Contribution

It introduces a resurgent transseries framework for the plasma's energy density, incorporating exponentially-suppressed sectors linked to quasinormal modes via AdS/CFT.

Findings

The energy density expansion is a multi-parameter transseries.

Nonhydrodynamic sectors correspond to quasinormal modes.

Resurgence allows recovery of nonhydrodynamic information from hydrodynamics.

Abstract

We show that the late-time expansion of the energy density of $\mathcal{N}=4$ supersymmetric Yang-Mills plasma at infinite coupling undergoing Bjorken flow takes the form of a multi-parameter transseries. Using the AdS/CFT correspondence we find a gravity solution which supplements the well known large proper-time expansion by exponentially-suppressed sectors corresponding to quasinormal modes of the AdS black-brane. The full solution also requires the presence of further sectors which have a natural interpretation as couplings between these modes. The exponentially-suppressed sectors represent nonhydrodynamic contributions to the energy density of the plasma. We use resurgence techniques on the resulting transseries to show that all the information encoded in the nonhydrodynamic sectors can be recovered from the original hydrodynamic gradient expansion.