Quantum Corrections to Thermodynamic Properties in the Large $N_f$ Limit of the Quark Gluon Plasma

Abstract

In this doctoral thesis we present the exact large $N_f$ calculation at next-to-leading order of the thermal interaction pressure of deconfined QCD for small and large quark chemical potential where the presence of the Landau pole is negligible numerically. For small values of the coupling we compare our results to existing perturbative results in the literature. Our numerical accuracy allows us to verify and even improve some of the existing perturbative coefficients by Freedman and McLerran for zero temperature or by Vuorinen for finite chemical potential and for linear and non-linear quark number susceptibilities, and to predict new coefficients to the sixth order in the coupling numerically that have not been calculated analytically yet. For larger couplings we determine where perturbation theory ceases to be applicable. For large chemical potential and small temperatures we enter the range of a so-called non-Fermi liquid, which in contrast to a classical Fermi liquid is dominated by long-range quasi-static transverse gauge-boson interactions. In this limit, we complete the previously known leading $T\ln T^{-1}$ contribution to the specific heat, and also go beyond this order to find a series involving anomalous fractional powers $T^{(3+2n)/3}$ caused by dynamical screening. We calculate their coefficients analytically up to order $T^{7/3}$ and find that these contributions determine the leading anomalous contribution in full QED and QCD (i.e. at finite $N_f$).