A0 Condensate in QCD

Abstract

A survey devoted to A,-condensate in gauge theories at high temperature is presented. Both theoretical foundations of the spontaneously generated condensate and known methods of its calculation are discussed. As the most important consequence, the S U ( N ) global symmetry breakdown is investigated in detail. The influence of A , on matter fields is studied in different aspects. Some new results concerning this subject are reported as well. 0. A. BORISENKO et al., A, Condensate in QCD know, there is no (mathematically) strict proof at the present time that the A,-condensate must disappear at high temperature. Nevertheless, we believe that calculation of the ( A , ) by different methods and, on the other hand, the derivation of the most significant consequences of such a condensate on multi-particle systems make our attempt quite justified. Besides, the appearance of the A,-condensate and the breakdown of global gauge symmetry can undoubtedly lead to significant improvement of our conception both of the high temperature behaviour of the strongly interacting matter and of the physics of gauge theories on the whole and surely have a connection to other problems currently under investigation (as, for instance, the infrared problem, the behaviour of quarks at non-zero baryonic number, etc.). All these questions will be considered in the paper.Let us begin with a comprehensive consideration of some known facts obtained from the studies of QCD. The Hamiltonian can be formally written as a sum of chromoelectric and chromomagnetic terms and has the following form in lattice version of the theory At finite temperature the behaviour of chromoelectric fields has been well studied both in the perturbative (in gz) region and especially in the non-perturbative one. As is generally known, in the strong coupling approximation the main contribution to the partition function results from the chromoelectric part in Eq. (l), because the chromomagnetic term, being proportional to g -2 , can be treated perturbatively in T . At high temperature, because of periodic boundary conditions, the gauge field configurations known as Polyakov loops develop a non-vanishing expectation value, which breaks global 2, symmetry ( Z ( N ) g l ) of the initial QCD-action and leads to deconfinement. As the Polyakov loops transform non-trivially under Z (Ql rotations, their non-zero expectation value could mean screening of Z(N)-charges (or static quarks) at T > zD (where KD is the critical temperature of the deconfinement phase transition). If this is the case, one may claim that there exists a physical quantity which characterizes the phenomenon of screening. This quantity is called the Debye mass and is defined in the continuum as the zero momentum limit of the time component of the vacuum polarization tensor, 1 g rni(T)= -II,,(L* 0, k,=0).(2)This definition gives a gauge invariant value for SU(N,) gauge theory with Nf massless fermions only in the lowest non-trivial order of the weak-coupling expansionThe calculation of no,, Eq.(2), in the two-loop ap...

Thermodynamic Potential With Condensate Fields in an Su(2) Model of QCD

“…Indeed, the infrared divergent term (see Eq. (6) of that paper) is reproduced from our expressions (24), (25) by expansion in powers of gH and subsequent integration in the proper time representation (14) with an infrared cutoff on the upper limit. Without expansion, the proper time integral for the real part of v G in (24), (25) converges, the parameter gH being the natural infrared regulator.…”

“…The contribution of the A 4 -potential is easily accounted for if we substitute iµ 1 → gA 4 , iµ 2 → g A4 2 for gluons or quarks, respectively, in expression (14). We remark that the role of the A 4 -potential in some way resembles that of the mass term, since for the gluon Lagrangian (4) we may write…”

“…We now examine the role of quarks concerning the stability of the condensate fields A 4 , H. In the chiral limit, when masses of quarks are zero, the one-loop effective potential of quarks is described according to (14) and (17) by the formula…”

“…Using (19) to separate the zero temperature term and introducing the proper time representation (14) we finally arrive at…”

“…11 On the other hand, at T > T c a new nonperturbative structure, which cannot be expressed in terms of field correlators, comes into play. This is the so-called Polyakov line 1,12 and the corresponding A 4 condensate 13 (see also the review article 14 ). Controversial evidence of the A 4 condensate has been published recently, part of which is in favor of its presence (see Refs.…”