DBI scalar field theory for QGP hydrodynamics

TL;DR

This paper models quark-gluon plasma hydrodynamics using a Dirac-Born-Infeld scalar field theory, capturing near-ideal fluid behavior and viscosity effects, and relates model parameters to QGP thermodynamics.

Contribution

It introduces a DBI scalar field framework for QGP hydrodynamics, incorporating viscosity and finite energy density effects, connecting the model to QGP thermodynamic properties.

Findings

Fluid near the shock is approximately ideal and conformal.

Adding a term inside the DBI action generates shear and bulk viscosities.

Parameter relations connect the model to QGP thermodynamics, such as temperature proportional to pion mass.

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 $\phi$ and its derivatives. One finds a relation between the parameters of the theory and the QGP thermodynamics, $\a/\b^2=\eta/(sT)$, and by fixing $\a$ and $\b$ from usual (low multiplicity) particle scattering, one finds $T\propto m_\pi$.