Abstract
We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized. We also explore the rapidity distribution of the energy density at hydrodynamization. This is far from boost-invariant and its width decreases as the non-conformality increases. Nevertheless, the velocity field at hydrodynamization is almost exactly boost-invariant regardless of the non-conformality. This result may be used to constrain the initialization of hydrodynamic fields in heavy ion collisions.
Highlights
The energy profile is determined by far-from-equilibrium physics beyond hydrodynamics, this decrease seems correlated with the bulk viscosity in our models
The fact that in this asymptotic regime tcondThyd is 5.18 times larger than thydThyd explicitly shows that a hydrodynamized plasma can be far from equilibrium, since between thyd and 5thyd hydrodynamics provides a good description of the stress tensor but the expectation value of the scalar operator is still far from its equilibrium value
This observation can be translated into consequences for hydrodynamic modellers of heavy ion collisions: even for configurations with significant rapidity dependence the initialization of the velocity field after the collision in a boost-invariant manner is well supported by our simulations
Summary
We will consider dynamics in a five-dimensional holographic model consisting of gravity coupled to a scalar field with a non-trivial potential. The second derivative of the potential at φ = 0 implies that the scalar field has mass m2 = −3/L2 therein. This means that, in the UV, this field is dual to an operator in the gauge theory, O, with dimension ∆UV = 3. The computation of the vacuum state can be simplified when the potential is derived from a super-potential as 4 −W (φ)2 In this case, the scalar profile φ(uFG) and the metric coefficient aFG(uFG) can be obtained from the equations uFG d aFG duFG. Where φ0 is an arbitrary constant with dimensions of mass that controls the magnitude of the non-normalizable mode of the scalar field. Throughout the paper we will use a redundant notation since we will use φ0 when we wish to emphasize the gravitational description and Λ when we wish to emphasize the gauge theory scale
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