Effective theory of relativistic fluids: Hydrodynamic Attractor and Bi-criticality

Abstract

We study relativistic hydrodynamics as an effective field theory to describe strongly interacting quantum field theories like QCD at long wavelengths. This approach can be used to model the Quark-Gluon Plasma formed in relativistic heavy-ion collisions with excellent agreement with observations. The Muller-Israel-Stewart formalism is a phenomenological extension of hydrodynamics which makes the theory causal, unlike finite order hydrodynamics. This introduces certain relaxation modes in the system which lead to the existence of an attractor solution to which the system flows rapidly before reaching equilibrium, even for initial conditions very far away. This is the hydrodynamic behaviour which could explain out of equilibrium fluids and the effectiveness of hydrodynamics in modelling QGP. Based on observations, to improve models of QGP, weakly interacting modes are coupled to a strongly interacting fluid through effective metrics of the two sectors, in the framework of semi-holography. Such coupled fluids demonstrate a second-order phase transition for a particular value of the coupling parameter. The critical behaviour of physical quantities like the entropy, and the hydrodynamic and non-hydrodynamic modes in the total system, is computed to understand the critical behaviour.