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.
Highlights
That a hydrodynamic description of the plasma is valid even when the anisotropy is still large [7]
The equal time 2-point function can be obtained from the length of space like geodesics which are anchored to the boundary of anti-de Sitter (AdS) space and extending into the bulk
In this work we extend the existing studies by investigating the time evolution of equal time 2-point functions and holographic entanglement entropy (HEE) in the colliding shock wave geometry for different initial conditions, carefully differentiating between wide, intermediate and narrow shocks, which turn out to have quite different phenomenology
Summary
The holographic setup we consider describes the collision of two sheets of energy having Gaussian shape in their direction of motion and which are homogeneous in the remaining two spatial directions. These shocks serve as caricatures of two highly Lorentz contracted nuclei which approach each other at the speed of light and induce non-abelian plasma formation as they collide. As usual the normalizable modes a4(v, y), b4(v, y) and f4(v, y) are undetermined by the near-boundary expansion and require a solution of the full bulk dynamics These coefficients in the asymptotic expansion determine the expectation value of the conserved and traceless stress energy tensor in the dual field theory [36]
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