DBI scalar field theory for QGP hydrodynamics

Abstract

A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η≃0) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ,P,η defined in terms of φ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α/β2=η/(sT), and by fixing α and β from usual (low multiplicity) particle scattering, one finds Ta mπ.