No abstract

We study two-dimensional QED with unequal charges at finite temperature, and show that there is a phase with a spontaneously broken Z n symmetry. In spite of this, we were not able to establish the presence of domain walls. The relevance for QCD in higher dimensions is discussed.

The thermodynamic free energy F is calculated for a gas whose particles are the quantum excitations of a piecewise uniform bosonic string. The string consists of two parts of length L I and L II , endowed with different tensions and mass densities, adjusted in such a way that the velocity of sound always equals the velocity of light. The explicit calculation is done under the restrictive condition that the tension ratio x = T I /T II approaches zero. Also, the length ratio s = L II /L I is assumed to be an integer. The expression for F is given on an integral form, in which s is present as a parameter. For large values of s, the Hagedorn temperature becomes proportional to the square root of s.

The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The string consists of three pieces I, II, III of equal length, endowed with different tensions and mass densities, but adjusted in such a way that the velocity of sound always equals the velocity of light. In this sense the string forms a relativistic mechanical system. In the present paper the string is subjected to the following analysis: the dispersion function is derived and the zero-point energy is regularized using ͑i͒ a contour integration technique, being most convenient for the generalization of the theory to the case of finite temperatures, and ͑ii͒ the Hurwitz -function technique, being usually the most compact method when the purpose is to calculate the Casimir energy numerically at Tϭ0. The energy, being always nonpositive, is shown graphically in some cases as functions of the tension ratios I/II and II/III. The generalization to finite temperature theory is also given.

The present work considers the phase transition between the confinement and "Coulomb" phases in U(1) gauge theory described by Wilson loop action. It was shown (using as an example the approximation of circular loops) that the critical coupling constant is rather independent of the regularization method. Taking into account the renormalization by artefact monopole contributions and the existence of strings in confinement phase assuming the maximal value of the effective fine structure constant equal to α max =π/12≈0.26, we obtain α c ≈0.204, in agreement with Monte Carlo lattice simulation result: α c ≈0.20. Such an approximate regularization independence ("universality") of the critical couplings is needed for the fine structure constant predictions claimed from "the multiple-point criticality principle".