Bulk viscosity of the massive Gross-Neveu model

Abstract

A calculation of the bulk viscosity for the massive Gross-Neveu model at zero fermion chemical potential is presented in the large-$N$ limit. This model resembles QCD in many important aspects: it is asymptotically free, has a dynamically generated mass gap, and for zero bare fermion mass it is scale invariant at the classical level (broken through the trace anomaly at the quantum level). For our purposes, the introduction of a bare fermion mass is necessary to break the integrability of the model, and thus to be able to study momentum transport. The main motivation is, by decreasing the bare mass, to analyze whether there is a correlation between the maximum in the trace anomaly and a possible maximum in the bulk viscosity, as recently conjectured. After numerical analysis, I find that there is no direct correlation between these two quantities: the bulk viscosity of the model is a monotonously decreasing function of the temperature. I also comment on the sum rule for the spectral density in the bulk channel, as well as on implications of this analysis for other systems.