Non-equilibrium Wilson loops in N=4 SYM

TL;DR

This paper investigates the behavior of rectangular Wilson loops in non-equilibrium states of N=4 SYM, revealing thermalization dynamics and quasinormal mode behavior analogous to black hole physics.

Contribution

It introduces a novel analysis of Wilson loops in non-equilibrium N=4 SYM, reducing the problem to a wave-equation with boundary conditions and identifying thermalization timescales.

Findings

Wilson loops approach a thermal form after time T=L/2

Bethe-Salpeter equation reduces to a wave-equation with quasinormal modes

Thermal behavior depends on initial state choice

Abstract

We consider rectangular Wilson loops in certain non-equilibrium quantum states in N=4 SYM at weak coupling, prepared with a quantum quench. We find that in the ladder approximation, the Bethe-Salpeter equation can be reduced to solving a massive 1+1 dimensional wave-equation with a leaking boundary condition leading to a quasinormal behavior analogous to what is found in studying dynamics of fields in black hole backrounds. Furthermore, we find that the Wilson loops with size L approach a thermal form after time T=L/2. The thermal form found in the current paper follows from the particular initial state chosen.