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DBI scalar field theory for QGP hydrodynamics

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 ($η\simeq 0$) 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 $u^μ, ρ,P,η$ defined in terms of $ϕ$ and its derivatives. One finds a relation between the parameters of the theory and the QGP thermodynamics, $\a/\b^2=η/(sT)$, and by fixing $\a$ and $\b$ from usual (low multiplicity) particle scattering, one finds $T\propto m_π$.