Abstract
Collisions of asymmetric planar shocks in maximally supersymmetric Yang-Mills theory are studied via their dual gravitational formulation in asymptotically anti-de 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].
Highlights
Perturbatively, either on the QCD or gravity side of the duality
In this paper we study the hydrodynamic flow resulting from asymmetric collisions of planar shocks in strongly coupled, maximally supersymmetric Yang-Mills theory
We find that the rapidity distribution of of the proper energy density for the asymmetric collisions is well approximated by the shifted geometric mean of the corresponding symmetric collision results, (ξ, τ ; w+, w−) ≈ (ξ − ξ(w+, w−; τ ), τ ; w+, w+) (ξ − ξ(w+, w−; τ ), τ ; w−, w−) 1/2 . (4.8)
Summary
Perturbatively, either on the QCD or gravity side of the duality. For example, corrections due to large but finite values of the ’t Hooft coupling λ = gY2 MN relevant for QCD can be calculated perturbatively on the gravity side, while the effects of non-conformality can be studied within QCD either perturbatively or using lattice gauge theory. Examples of observables with relatively modest corrections due to finite coupling and non-conformality effects include the viscosity to entropy density ratio [18], 4πη/s = 1 + 15 ζ(3) λ−3/2 ≈ 1.4 for λ ≈ 12, and the short hydrodynamization time predicted by AdS/CFT duality based on calculations of the lowest quasinormal mode (QNM) frequency [19]. For the latter quantity, finite coupling corrections are larger than for η/s, but not so much as to change the picture qualitatively. The energy scale μ characterizes the transverse energy density of each incoming shock and is defined by the longitudinally integrated (rescaled) energy density of either incoming shock, μ3 ≡ dz T 00(z ± t)incoming−shock
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