C.P. Korthals Altes

Reduced model for large N continuum field theories

Abstract We formulate a reduced model for large N gauge and non-gauge field theories, in even space-time dimensions. The model is regularised in a rotationally invariant way, and the equivalence of the model with the ordinary one is exhibited in perturbation theory.

Asymptotic freedom scales for any single plaquette action

Abstract We analyze with the background field method the ratio of the renormalization group scales in the continuum, Λ cont , and on the lattice, Λ L . We find, in contrast to an earlier background field calculation, good agreement with conventional calculations, extend the result in analytic form to any acceptable lattice action and find actions where the ratio can take any value. Comparison with available computer data is made. Qualitative agreement is found.

Zero-momentum contribution to wilson loops in periodic boxes

Abstract We compute the zero-momentum finite-size effects in non-abelian gauge theories. In some cases, these effects are to lowest-order identical for lattice and continuum theories and are of the order of a few percent for an SU(3) gauge theory in four dimensions.

Constrained effective potential in hot QCD

Abstract Constrained effective potentials in hot gauge theory give the probability that a configuration p of the order parameter (Polyakov loop) occurs. They are important in the analysis of surface effects and bubble formation in the plasma. The vector potential appears non-linearly in the loop; in weak coupling the linear term gives rise to the traditional free-energy graphs. But the non-linear terms generate insertions of the constrained modes into the free-energy graphs, through renormalisations of the Polyakov loop. These insertions are gauge dependent and are necessary to cancel the gauge dependence of the free-energy graphs. The latter is shown, through the BRST identities, to have again the form of constrained mode insertions. We stress that the effective action, without this insertion, is gauge variant and gives quite deceptive information. Amongst more it follows, that absolute minima of the potential are at the center group values of the loop, once the insertion is done. We evaluate the two-loop contributions for SU( N ) gauge theories, with and without quarks, for the full domain of the N − 1 variables.

Duality for Z(N) gauge theories

Abstract The duality properties of simple Z( N ) gauge theories are discussed. For N ⩽ 4 we find self duality in four dimensions and we give the transition points. For N > 4 these systems are not self dual. Also, the order parameter is discussed. The general Z( N ) gauge theory is found to be self dual for all N .

More structure in the string tension

Abstract Monte Carlo data for the string tension of mixed action SU(2) gauge theory are confronted with strong coupling expansions and weak coupling universality constraints. It turns out that either the Wilson action is unique in that it scales precociously as is usually accepted, or that there is additional structure in the Wilson string tension (and a larger value of the Λ-parameter). After finishing this work we received a preprint by Bhanot and Dashen, whose string tension data are shown to fit the strong coupling expansion. This explains their anomaly in the renormalisation group scale.

Finite temperature Z(N) phase transition with Kaluza-Klein gauge fields

If SU(N) gauge fields live in a world with a circular extra dimension, coupling there only to adjointly charged matter, the system possesses a global Z(N) symmetry. If the radius is small enough such that dimensional reduction takes place, this symmetry is spontaneously broken. It turns out that its fate at high temperatures is not easily decided with straightforward perturbation theory. Utilising non-perturbative lattice simulations, we demonstrate here that the symmetry does get restored at a certain temperature T_c, both for a 3+1 and a 4+1 dimensional world (the latter with a finite cutoff). To avoid a cosmological domain wall problem, such models would thus be allowed only if the reheating temperature after inflation is below T_c. We also comment on the robustness of this phenomenon with respect to small modifications of the model.

Local order parameter in twisted gauge fields

We establish a new order parameter signaling phase transitions in lattice gauge theories which is especially devised for computer simulation. It is used to investigate phase diagrams for several gauge groups.

Energy spectrum of SU(2) Yang-Mills fields with space-like symmetric twist

Abstract We compute the energy levels of an SU(2) Yang-Mills field in perturbation theory to order g 2 , for a box of finite size and symmetric twist m =(1, 1, 1) . A cubic-invariant spectrum results, with almost degenerate E ++ and T 2 ++ levels. Various suggestions for further MC measurements are made.

Domain walls and perturbation theory in high temperature gauge theory: SU(2) in (2+1)-dimensions

We study the detailed properties of Z{sub 2} domain walls in the deconfined high-temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter g{sup 2}/T is close to unity. The quantities studied include the surface tension, the action density profiles, roughening, and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool. {copyright} {ital 1997} {ital The American Physical Society}