Evolution of nonlocal observables in an expanding boost-invariant plasma

TL;DR

This paper analytically studies how nonlocal observables like two-point functions, Wilson loops, and entanglement entropy evolve over time in an expanding strongly coupled plasma, revealing viscosity effects and constraints on hydrodynamic validity.

Contribution

It provides the first analytical analysis of late-time behavior of nonlocal observables in an expanding plasma including viscosity effects.

Findings

Two-point functions decay exponentially at late times.

Transverse observables are unaffected by shear viscosity.

Longitudinal observables show nonmonotonic behavior influenced by viscosity.

Abstract

Using the AdS/CFT correspondence, we compute analytically the late-time behavior of two-point functions, Wilson loops and entanglement entropy in a strongly coupled $\mathcal{N}=4$ super-Yang-Mills plasma undergoing a boost-invariant expansion. We take into account the effects of first order dissipative hydrodynamics and investigate the effects of the (time-dependent) shear viscosity on the various observables. The two-point functions decay exponentially at late times and are unaffected by the viscosity if the points are separated along the transverse directions. For longitudinal separation we find a much richer structure. In this case the exponential is modulated by a nonmonotonic function of the rapidities and a dimensionless combination of the shear viscosity and proper time. We show that this peculiar behavior constrains the regime of validity of the hydrodynamical expansion. In addition, similar results are found for certain Wilson loops and entanglement entropies.