Hard Thermal Loops , Gauged WZNW - Action and the Energy of Hot Quark - Gluon Plasma

Abstract

The generating functional for hard thermal loops in Quantum Chromodynamics is rewritten in terms of a gauged Wess-Zumino-Novikov-Witten action by introducing an auxiliary field. This shows in a simple way that the contribution of hard thermal loops to the energy of the quark-gluon plasma is positive. This research was supported in part by the U.S. Department of Energy. ∗ Address after September 1, 1993: Physics Department, City College of the CUNY, Convent Avenue at 138 Street, New York, NY 10031. The effective action or generating functional Γ for hard thermal loops in Quantum Chromodynamics (QCD) has been the subject of many recent investigations [1-4]. We have shown that Γ is essentially given by the eikonal for a Chern-Simons (CS) gauge theory [3]. Γ is a nonlocal functional of the gauge potential Aμ and leads to new effective propagators and vertices. These effective propagators and vertices help to carry out the reorganization (and partial summation) of thermal perturbation theory necessary to ensure that all contributions to a given order in the coupling constant are consistently included. Further, many of the properties of the quark-gluon plasma at high temperature can be understood in terms of the action S = ∫ 1 4 F 2 + Γ[A] (1) where we add Γ to the usual Yang-Mills action. The action (1) gives a gauge invariant description of Debye screening and plasma waves. Also, with a proper i -prescription, the equations of motion following from (1) (which are also nonlocal) can describe Landau damping [4]. Clearly further investigation of Γ is interesting both for the programme of resummation of perturbation theory and for clarifying properties of the quark-gluon plasma at high temperature. In this paper, we introduce an auxiliary field and rewrite Γ in terms of a gauged Wess-Zumino-Novikov-Witten (WZNW) theory. This field is actually defined on a sixdimensional space. The elimination of the auxiliary field via its equations of motion leads back to (1) with Γ expressed in terms of the potentials. The introduction of the auxiliary field has the advantage that the equations of motion are local. This facilitates further analysis since the quark-gluon plasma (at high temperature) can now be described by a gauge theory coupled, in a local and more or less standard way, to an auxiliary field. We also obtain the energy functional and show that it is positive for all physical field configurations, a question which has been of some concern recently [5]. This rewriting of the theory may also help in setting up the resummed perturbation theory; new auxiliary field propagators and vertices can be used to incorporate hard thermal loop effects. We begin by recalling some of the essential results of ref.[3]. Q, Q′ will denote the null vectors Qμ = (1, ~ Q), Qμ = (1,−~ Q) with ~ Q · ~ Q = 1. We introduce the light-

Cite this paper

@inproceedings{NairHardTL, title={Hard Thermal Loops , Gauged WZNW - Action and the Energy of Hot Quark - Gluon Plasma}, author={Vinit P. Nair} }