We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local potential approximation. This approximation reproduces the perturbative results for the screening mass and the pressure up to order g 3 , and starts to differ at order g 4 . The method allows a smooth extrapolation to the regime where the coupling is not small, very similar to that obtained from a simple self-consistent approximation.

Long-range quasi-static gauge-boson interactions lead to anomalous (non-Fermiliquid) behavior of the specific heat in the low-temperature limit of an electron or quark gas with a leading T ln T −1 term. We obtain perturbative results beyond the leading log approximation and find that dynamical screening gives rise to a low-temperature series involving also anomalous fractional powers T (3+2n)/3 . We determine their coefficients in perturbation theory up to and including order T 7/3 and compare with exact numerical results obtained in the large-N f limit of QED and QCD. PACS numbers: 11.10.Wx, 12.38.Mh, 71.45.Gm, 11.15.Pg It has been established long ago [1] in the context of a nonrelativistic electron gas that the only weakly screened low-frequency transverse gauge-boson interactions lead to a qualitative deviation from Fermi liquid behavior. A particular consequence of this is the appearance of an anomalous contribution to the low-temperature limit of entropy and specific heat proportional to αT ln T −1 [1, 2, 3], but it was argued that the effect would be probably too small for experimental detection.More recently, it has been realized that analogous non-Fermi-liquid behavior in ultradegenerate QCD is of central importance to the magnitude of the gap in color superconductivity [4,5,6], and it has been pointed out [7] that the anomalous contributions to the low-temperature specific heat may be of interest in astrophysical systems such as neutron or protoneutron stars, if they involve a normal (non-superconducting) degenerate quark matter component.So far only the coefficient of the αT ln T −1 term in the specific heat has been determined (with Ref.[3] correcting the result of Ref.[1] by a factor of 4), but not the complete argument of the leading logarithm. While the existence of the T ln T −1 term implies that there is a temperature range where the entropy or the specific heat exceeds the ideal-gas value, without knowledge of the constants "under the log" it is impossible to give numerical values for the required temperatures.Furthermore, a quantitative understanding of these anomalous contributions is also of interest with regard to the recent progress made in high-order perturbative calculations of the pressure (free energy) of QCD at nonzero temperature and chemical potential [8], where it has been found that dimensional reduction techniques work remarkably well except for a narrow strip in the T -µ-plane around the T = 0 line.In the present Letter we report the results of a calculation of the low-temperature entropy and specific heat for ultradegenerate QED and QCD which goes beyond the leading log approximation. Besides completing the leading logarithm, we find that for T /µ ≪ g ≪ 1, where g is either the strong or the electromagnetic coupling constant, the higher terms of the low-temperature series involve also anomalous fractional powers T (3+2n)/3 , and we give their coefficients through order T 7/3 . Our starting point is an expression for the thermodynamic potential of QED and QCD

We present the first 3+1 dimensional simulations of non-Abelian plasma instabilities in gaugecovariant Boltzmann-Vlasov equations for the QCD gauge group SU(3) as well as for SU(4) and SU(5). The real-time evolution of instabilities for a plasma with stationary momentum-space anisotropy is studied using a hard-loop effective theory that is discretized in the velocities of hard particles. We find that the numerically less expensive calculations using the group SU(2) essentially reproduce the nonperturbative dynamics of non-Abelian plasma instabilities with higher rank gauge groups provided the mass parameters of the corresponding hard-loop effective theories are the same. In particular we find very similar spectra for the turbulent cascade that forms in the strong-field regime, which is associated with an approximately linear growth of energy in collective fields. The magnitude of the linear growth however turns out to increase with the number of colors.

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