Hot gluon plasma at large distances

Abstract

The authors study some general features of a pure gluon plasma in the regime of high temperature and large distances. Starting from the continuum four-dimensional Yang-Mills theory in the imaginary-time formalism, they outline how it becomes dimensionally reduced to a three-dimensional theory in the above regime. They discuss the effects of electric gluons on this reduction and show that, in such a regime and to all perturbative orders, electric gluons in internal lines and, in particular, a direct quartic coupling of such gluons, yield subdominant contributions. They carry out a new renormalisation group analysis and find that the only renormalisation group equation in that regime is the trivial one, associated with superrenormalisable theories. It is, then, argued that there are no free magnetic gluons in that regime. Alternatively, they test the stability properties of the nonreduced Yang-Mills theory in the limit of high temperature and large distance, by calculating the damping constant of the gluon plasma in the real-time formalism. They find the plasma to be unstable to small oscillations of the colour field. They argue that this is what could be expected for a system with a confined phase such as the magnetic gluon sector of the dimensionally reduced Yang-Mills theory.