• DOI:10.1103/PhysRevD.94.025014
• Corpus ID: 119301668

DBI scalar field theory for QGP hydrodynamics

@article{Nastase2015DBISF,
  title={DBI scalar field theory for QGP hydrodynamics},
  author={Horatiu Nastase},
  journal={Physical Review D},
  year={2015},
  volume={94},
  pages={025014}
}

• H. Nastase
• Published 16 December 2015
• Mathematics
• Physical Review D

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 ($\ensuremath{\eta}\ensuremath{\simeq}0$) 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 behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with ${u}^{\ensuremath{\mu}},\ensuremath{\rho},P,\ensuremath{\eta}$ defined in terms of $\ensuremath{\phi}$ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, $\ensuremath{\alpha}/{\ensuremath{\beta}}^{2}=\ensuremath{\eta}/(sT)$, and by fixing $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ from usual (low multiplicity) particle scattering, one finds $T\ensuremath{\propto}{m}_{\ensuremath{\pi}}$.