Collisions of asymmetric planar shocks in maximally supersymmetric Yang-Mills theory are studied via their dual gravitational formulation in asymptotically antide Sitter spacetime. The post-collision hydrodynamic flow is found to be very well described by appropriate means of the results of symmetric shock collisions. This study extends, to asymmetric collisions, previous work of Chesler, Kilbertus, and van der Schee examining the special case of symmetric collisions [1]. Given the universal description of hydrodynamic flow produced by asymmetric planar collisions one can model, quantitatively, non-planar, non-central collisions of highly Lorentz contracted projectiles without the need for computing, holographically, collisions of finite size projectiles with very large aspect ratios. This paper also contains a pedagogical description of the computational methods and software used to compute shockwave collisions using pseudo-spectral methods, supplementing the earlier overview of Chesler and Yaffe [2].

We consider the second Rényi entropy S (2) in pure lattice gauge theory with SU (2), SU (3) and SU (4) gauge groups, which serves as a first approximation for the entanglement entropy and the entropic C-function. We compare the results for different gauge groups using scale setting via the string tension. We confirm that at small distances l our approximation for the entropic C-function C(l), calculated for the slab-shaped entangled region of width l, scales as N 2 c − 1 in accordance with its interpretation in terms of free gluons. At larger distances l C(l) is found to approach zero for Nc = 3, 4, somewhat more rapidly for Nc = 4 than for Nc = 3. This finding supports the conjectured discontinuity of the entropic C-function in the large-N limit, which was found in the context of AdS/CFT correspondence and which can be interpreted as transition between colorful quarks and gluons at small distances and colorless confined states at long distances. On the other hand, for SU (2) gauge group the long-distance behavior of the entropic C-function is inconclusive so far. There exists a small region of lattice spacings yielding results consistent with Nc = 3, 4, while results from other lattice spacings deviate without clear systematics. We discuss several possible causes for discrepancies between our results and the behavior of entanglement entropy in holographic models.

This paper discusses possible phenomenological implications for p+A and A+A collisions of the results of recent numerical AdS/CFT calculations examining asymmetric collisions of planar shocks. In view of the extreme Lorentz contraction, we model highly relativistic heavy ion collisions (HICs) as a superposition of collisions between many near-independent transverse "pixels" with differing incident longitudinal momenta. It was found that also for asymmetric collisions the hydrodynamization time is in good approximation a proper time, just like for symmetric collisions, depending on the geometric mean of the longitudinally integrated energy densities of the incident projectiles. For realistic collisions with fluctuations in the initial energy densities, these results imply a substantial increase in the hydrodynamization time for highly asymmetric pixels. However, even in this case the local hydrodynamization time still is significantly smaller than perturbative results for the thermalization time.