Casimir Scaling and String Breaking in G(2) Gluodynamics

We study the potential energy between static charges in G(2) gluodynamics in three and four dimensions. Our work is based on an efficient local hybrid Monte-Carlo algorithm and a multi-level L\"uscher-Weisz algorithm with exponential error reduction to accurately measure expectation values of Wilson- and Polyakov loops. Both in three and four dimensions we show that at intermediate scales the string tensions for charges in various G(2)-representations scale with the second order Casimir. In three dimensions Casimir scaling is confirmed within one percent for charges in representations of dimensions 7, 14, 27, 64, 77, 77', 182 and 189 and in 4 dimensions within 5 percent for charges in representions of dimensions 7, 14, 27 and 64. In three dimensions we detect string breaking for charges in the two fundamental representations. The scale for string breaking agrees very well with the mass of the created pair of glue-lumps.Comment: 20 pages, 17 figure

Confinement and the quark Fermi-surface in SU(2N) QCD-like theories

Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrated by means of a simple quark model.Comment: 5 pages, 2 figures, revised journal versio

Witten-Veneziano Relation for the Schwinger Model

The Witten-Veneziano relation between the topological susceptibility of puregauge theories without fermions and the main contribution of the completetheory and the corresponding formula of Seiler and Stamatescu with theso-called contact term are discussed for the Schwinger model on a circle. Usingthe (Euclidean) path integral and the canonical (Hamiltonian) approaches atfinite temperatures we demonstrate that both formulae give the same result inthe limit of infinite volume and (or) zero temperature