Exploring nonlocal observables in shock wave collisions

TL;DR

This study investigates the time evolution of nonlocal observables like 2-point functions and entanglement entropy during shock wave collisions in strongly coupled gauge theories, revealing different phenomenologies and phases of plasma formation.

Contribution

It introduces a numerical analysis of geodesics and extremal surfaces in dynamical shockwave backgrounds, distinguishing shock types and their effects on nonlocal observables in holographic models.

Findings

Entanglement entropy can serve as an order parameter for phase transitions in plasma formation.

Different shock profiles lead to distinct entanglement and correlation behaviors.

2-point functions can probe the black hole interior, unlike entanglement entropy.

Abstract

We study the time evolution of 2-point functions and entanglement entropy in strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills theory in the large N and large 't Hooft coupling limit using AdS/CFT. On the gravity side this amounts to calculating the length of geodesics and area of extremal surfaces in the dynamical background of two colliding gravitational shockwaves, which we do numerically. We discriminate between three classes of initial conditions corresponding to wide, intermediate and narrow shocks, and show that they exhibit different phenomenology with respect to the nonlocal observables that we determine. Our results permit to use (holographic) entanglement entropy as an order parameter to distinguish between the two phases of the cross-over from the transparency to the full-stopping scenario in dynamical Yang-Mills plasma formation, which is frequently used as a toy model for heavy ion collisions. The time evolution of entanglement entropy allows to discern four regimes: highly efficient initial growth of entanglement, linear growth, (post) collisional drama and late time (polynomial) fall off. Surprisingly, we found that 2-point functions can be sensitive to the geometry inside the black hole apparent horizon, while we did not find such cases for the entanglement entropy.