DBI scalar field theory for QGP hydrodynamics

Abstract

A way to describe the hydrodynamics of the quark-gluon plasma using a 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 ($\eta \simeq 0$) 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 behaviour of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with $u^{\mu },\rho ,P,\eta$ defined in terms of $\varphi$ and its derivatives. One finds a relation between the parameters of the theory and the QGP thermodynamics, $\text{a}/{\text{b}}^2=\eta /(sT)$, and by fixing $\text{a}$ and $\text{b}$ from usual (low multiplicity) particle scattering, one finds $T\propto m_{\pi }$.

Comments: 19 pages, no figures; clarifications added in section 4