Infrared Properties of the Hot Gauge Theory after Symmetry Breaking

Abstract

It is shown that the fictitious infrared pole is eliminated from the hot gauge theory which acquires a new vacuum after the global gauge symmetry spontaneously broken. The nonzero W-condensate appears and leads to a screening of the chromomagnetic forces through the scenario with the standard magnetic mass. The strong infrared divergences which usually accompany the multi-loop pertur­ bative calculations with a hot non-Abelian gauge theory are an intrinsic property of SU(N)-gluodynamics and determine many of its peculiarities. Unfortunately, their essence remains unclear, although the infrared properties of the Yang-Mills theory at T-=1=0 have been intensively studied during recent years. At T-=1=0 the infrared problem in QCD is more pronounced since, unlike QFT, the leading infrared diver­ gences are power-like and most of the Green functions calculated perturbatively demonstrate the fictitious infrared pole when p4 = 0 and IPI ~ g 2 T. This singularity (originally found in papers 1) and 2)) is strongly sensitive to the gauge chosen although it cannot be removed through its redefinition and remains practically the same when the radiative corrections are taken into account. In the present paper we study the infrared properties of the hot SU(2)-model which acquires a new vacuum with the nonzero W-condensate after the global gauge symmetry spontaneously broken. Within this scenario the infrared fictitious pole being a signal of the infrared instability for the unbroken gauge theory is eliminated at the beginning and the standard magnetic mass arises already on the one-loop level. The broken gauge theory demonstrates the correct infrared properties but unfortu­ nately all its infrared limits are strongly gauge-dependent at least within a pertur­ bative expansion. This dependence seems not to be occasional and its appearance should be carefully investigated although it is necessary to remember (see, e.g., Ref. 3) for details) that all the standard nonperturbative infrared limits are gauge­ dependent as well. § 2. General formalism and definition Our formalism is built by using the standard Green function technique at T-=1=0 in the background gauge with an arbitrary parameter ~- The effective action W(A) is defined as a functional integral over periodic gauge and ghost fields