A semi-holographic model for heavy-ion collisions

Abstract

We develop a semi-holographic model for the out-of-equilibrium dynamics during the partonic stages of an ultrarelativistic heavy-ion collision. The model combines a weakly-coupled hard sector, involving gluon modes with energy and momenta of the order of the saturation momentum and relatively large occupation numbers, with a strongly-coupled soft sector, which physically represents the soft gluons radiated by the hard partons. The hard sector is described by perturbative QCD, more precisely, by its semi-classical approximation (the classical Yang-Mills equations) which becomes appropriate when the occupation numbers are large. The soft sector is described by a marginally deformed conformal field theory, which in turn admits a holographic description in terms of classical Einstein's equations in $AdS_5$ with a minimally coupled massless `dilaton'. The model involve two free parameters which characterize the gauge-invariant couplings between the hard and soft sectors. Via these couplings, the hard modes provide dynamical sources for the gravitational equations at the boundary of $AdS_5$ and feel the feedback of the latter as additional soft sources in the classical Yang-Mills equations. Importantly, the initial conditions for this coupled dynamics are fully determined by the hard sector alone, i.e. by perturbative QCD, and are conveniently given by the color glass condensate (CGC) effective theory. We also develop a new semi-holographic picture of jets in the QGP by attaching a non-Abelian charge to the endpoint of the trailing string in $AdS_5$ representing a heavy quark. This leads to modified Nambu-Goto equations for the string which govern the (collisional and radiative) energy loss by the heavy quark towards both hard and soft modes.