Bengt Petersson

We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c<T<T_c we enter the critical region, where the critical properties of the correlations are fixed by universality to be those of the two dimensional three state Potts model. Nevertheless, by calculating the critical lattice coupling, we show that the ratio of the critical temperature to the square root of the zero temperature string tension, where the latter is taken from the literature, remains very near to the string model prediction.

We investigate semiclassical properties of space-time geometry of the low energy limit of reduced four dimensional supersymmetric Yang-Mills integrals using Monte-Carlo simulations. The limit is obtained by an one-loop approximation of the original Yang-Mills integrals leading to an effective model of branched polymers. We numerically determine the behaviour of the gyration radius, the two-point correlation function and the Polyakov-line operator in the effective model and discuss the results in the context of the large-distance behaviour of the original matrix model.

We analyze a two dimensional SU(3) gauge model of Wilson lines as a dimensionally reduced model of high temperature QCD_3. In contrast to perturbative dimensional reduction it has an explicit global Z(3) symmetry in the action. The phase diagram of the model is studied in the space of two free parameters used to describe the self interaction of the Wilson lines. In addition to the confinement-deconfinement transition, the model also exhibits a new Z(3)-breaking phase. These findings are obtained by numerical simulations, and supported by a perturbative calculation to one loop. A screening mass from Polyakov loop correlations is calculated numerically. It matches the known QCD_3 mass in a domain of parameters belonging to the normal deconfined phase.

We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. In the symmetric phase of its global Z_2 symmetry, two colourless boundstates, even and odd under Z_2, are identified. Their respective contributions (poles) in correlation functions of local composite operators A_n of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the p=2 operators into polynomials in p=1 operators. No sizable signal in any A_n correlation can be attributed to 1/n times a Debye screening length associated with n elementary fields. These results are quantitatively consistent with the picture of scalar ``matter'' fields confined within colourless boundstates whose residual ``strong'' interactions are very weak.

In this talk I will first give a short discussion of some lattice results for QCD at finite temperature. I will then describe in some detail the technique of dimensional reduction, which in principle is a powerful technique to obtain results on the long distance properties of the quark-gluon plasma. Finally I will describe some new results, which test the technique in a simpler model, namely three dimensional gauge theory.

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increaseof the static S-wave pair correlation with decreasing temperature is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. The evidence for this transition is weak: If it exists, its temperature is very low and depends weakly on the band filling near half filling. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Pade approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data.