Effect of the GUP on the Entropy, Speed of Sound, and Bulk to Shear Viscosity Ratio of an ideal QGP

Abstract

In this work we compute the entropy density, speed of sound, and the resulting impact on the bulk viscosity to shear viscosity ratio of an ideal Quark Gluon Plasma when the effects of a generalized uncertainty principle are taken into consideration. When the parameter of the generalized uncertainty principle tends to zero, i.e., $\alpha \to 0$, we obtain the value of the speed of sound for the ideal gas of massless particles, i.e., $c_s^2\to 1/3$, and we recover the expected result that the bulk viscosity $\zeta \to 0$ when $\alpha \to 0$. In addition, in the high temperature limit, i.e., $T\to \infty$, the speed of sound satisfies the equation $c_s^2\to 1/4$. The consequence this has on the bulk viscosity is that in the high temperature limit, the ratio of the bulk to shear viscosity $\zeta /\eta \to 5/48$. Our results suggest that the GUP introduces a scale into the system breaking the a priori conformal invariance of a system of massless noninteracting particles.

Comments: 7 pages, no figures, REVTeX 4, to appear in NPB