DIMENSIONAL REDUCTION AT HIGH TEMPERATURE FOR FERMIONS

The concept of dimensional reduction in the high temperature regime is generalized to static Green's functions of composite operators that contain fermionic fields. The recognition of a natural kinematic region where the lowest Matsubara modes are close to their mass-shell, and the ultraviolet behavior of the running coupling constant of the original theory are crucial for providing the necessary scale hierarchy. The general strategy is illustrated in the asymptotically-free Gross-Neveu model in 1+1 dimensions, where we verify that dimensional reduction occurs to the leading order in $g^2(T)$. We also find, in the same model, that the scale parameter characterizing the dependence on temperature of the coupling constant in the reduced theory, $\Lambda_T$, is considerably smaller than $\Lambda_{\bar{\text{MS}}}$. Implications of our results for QCD are also discussed.