Quantum Link Models: A Discrete Approach to Gauge Theories

We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed matter physics. When formulated with a fifth Euclidean dimension, universality arguments suggest that dimensional reduction to four dimensions occurs. Hence, quantum link models are also reformulations of ordinary quantum field theories and are applicable to particle physics, for example to QCD. The configuration space of quantum link models is discrete and hence their numerical treatment should be simpler than that of ordinary lattice gauge theories with a continuous configuration space.Comment: 18 pages, Latex, no figures, final version to appear in Nuclear Physics B, references to earlier work by Horn, Orland and Rohrlich include

Level-Rank Duality in Chern-Simons Theory from a Non-Supersymmetric Brane Configuration

We derive level-rank duality in pure Chern-Simons gauge theories from a non-supersymmetric Seiberg duality by using a non-supersymmetric brane configuration in type IIB string theory. The brane configuration consists of fivebranes, N D3 antibranes and an O3 plane. By swapping the fivebranes we derive a 3d non-supersymmetric Seiberg duality. After level shifts from loop effects, this identifies the IR of Sp(2N)_{2k-2N+2} and Sp(2k-2N+2)_{-2N} pure Chern-Simons theories, which is a level-rank pair. We also derive level-rank duality in a Chern-Simons theory based on a unitary group.Comment: 10 pages, 3 figure

On the Configuration Space of Gauge Theorie

We investigate the structure of the configuration space of gauge theories and its description in terms of the set of absolute minima of certain Morse functions on the gauge orbits. The set of absolute minima that is obtained when the background connection is a pure gauge is shown to be isomorphic to the orbit space of the pointed gauge group. We also show that the stratum of irreducible orbits is geodesically convex, i.e. there are no geometrical obstructions to the classical motion within the main stratum. An explicit description of the singularities of the configuration space of SU(2) theories on a topologically simple space-time and on the lattice is obtained; in the continuum case we find that the singularities are conical and that the singular stratum is isomorphic to a Z_2 orbifold of the configuration space of electrodynamics.Comment: 22 pages [A4] in LaTeX, HD-THEP-94-11, NIKHEF-H/94-1

A new example of N=2 supersymmetric Landau-Ginzburg theories: the two-ring case

The new example of N=2 supersymmetric Landau-Ginzburg theories is considered when the critical values of the superpotential w(x) form the regular two-ring configuration. It is shown that at the deformation, which does not change the form of this configuration, the vacuum state metric satisfies the equation of non-Abelian 2 x 2 Toda system.Comment: LaTeX, 13p

Supersymmetric Gauge Theories from Branes and Orientifold Six-planes

We study brane configurations in the presence of orientifold six-planes. After deriving the curves for N=2 supersymmetric SU(Nc) gauge theories with one flavor in the symmetric or antisymmetric representation and Nf fundamental flavors, we rotate the brane configuration, reducing the supersymmetry to N=1. For the case of an antisymmetric flavor and less than two fundamental flavors, nonperturbative effects lead to a brane configuration that is topologically a torus. Using the description of the orientifold six-planes as Dn singularities we discuss the Higgs branches for N=2 brane configurations with Sp/SO gauge groups and the related N=1 theories with tensor representations.Comment: 30 pages (harvmac b-mode), 5 figures, (v2 minor corrections), (v3 sign error corrected