Laplacian Abelian Projection: Abelian dominance and Monopole dominance

A comparative study of Abelian and Monopole dominance in the Laplacian and Maximally Abelian projected gauges is carried out. Clear evidence for both types of dominance is obtained for the Laplacian projection. Surprisingly, the evidence is much more ambiguous in the Maximally Abelian gauge. This is attributed to possible ``long-distance imperfections'' in the maximally abelian gauge fixing.Comment: LATTICE98(confine), 3 page

Gauge invariant extremization on the lattice

Recently, a method was proposed and tested to find saddle points of the action in simulations of non-abelian lattice gauge theory. The idea, called `extremization', is to minimize \int(\dl S/\dl A_\mu)^2. The method was implemented in an explicitly gauge variant way, however, and gauge dependence showed up in the results. Here we show how extremization can be formulated in a way that preserves gauge invariance on the lattice. The method applies to any gauge group and any lattice action. The procedure is worked out in detail for the standard plaquette action with gauge groups U(1) and SU(N).Comment: 7 pages, LaTeX, Oxford preprint OUTP-92-16

A lattice field theoretical model for high-TcT_c superconductivity

We present a 2+1-dimensional lattice model for the copper oxide superconductors and their parent compounds, in which both the charge and spin degrees of freedom are treated dynamically. The spin-charge coupling parameter is associated to the doping fraction in the cuprates. The model is able to account for the various phases of the cuprates and their properties, not only at low and intermediate doping but also for (highly) over-doped compounds. We acquire a qualitative understanding of high-$T_c$ superconductivity as a Bose-Einstein condensation of bound charge pairs.Comment: talk presented in the Lattice 97 conferenc

Phase diagram and quasiparticles of a lattice SU(2) scalar-fermion model in 2+1 dimensions

The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in 211 dimensions is studied numerically and with mean-field methods. Special attention is devoted to the strong coupling regime. We have developed a new method to adapt the hybrid Monte Carlo algorithm to the O(3) non-linear σ model constraint. The charged excitations in the various phases are studied at the mean-field level. Bound states of two charged fermions are found in a strongly coupled paramagnetic phase. On the other hand, in the strongly coupled antiferromagnetic phase fermionic excitations around momenta (±π/2, ±π/2, ±π/2) emerge

A new mechanism of mass protection for fermions

We present a way of protecting a Dirac fermion interacting with a scalar (Higgs) field from getting a mass from the vacuum. It is obtained through an implementation of translational symmetry when the theory is formulated with a momentum cutoff, which forbids the usual Yukawa term. We consider that this mechanism can help to understand the smallness of neutrino masses without a tuning of the Yukawa coupling. The prohibition of the Yukawa term for the neutrino forbids at the same time a gauge coupling between the right-handed electron and neutrino. We prove that this mechanism can be implemented on the lattice.Comment: LATTICE99(Higgs,Yukawa,SUSY), 3 page

Modified iterative versus Laplacian Landau gauge in compact U(1) theory

Compact U(1) theory in 4 dimensions is used to compare the modified iterative and the Laplacian fixing to lattice Landau gauge in a controlled setting, since in the Coulomb phase the lattice theory must reproduce the perturbative prediction. It turns out that on either side of the phase transition clear differences show up and in the Coulomb phase the ability to remove double Dirac sheets proves vital on a small lattice.Comment: 14 pages, 8 figures containing 23 graphs, v2: 2 figures removed, 2 references adde

A Magnetic Monopole in Pure SU(2) Gauge Theory

The magnetic monopole in euclidean pure SU(2) gauge theory is investigated using a background field method on the lattice. With Monte Carlo methods we study the mass of the monopole in the full quantum theory. The monopole background under the quantum fluctuations is induced by imposing fixed monopole boundary conditions on the walls of a finite lattice volume. By varying the gauge coupling it is possible to study monopoles with scales from the hadronic scale up to high energies. The results for the monopole mass are consistent with a conjecture we made previously in a realization of the dual superconductor hypothesis of confinement.Comment: 33 pages uufiles-compressed PostScript including (all) 12 figures, preprint numbers ITFA-93-19 (Amsterdam), OUTP-93-21P (Oxford), DFTUZ/93/23 (Zaragoza

Writhe of center vortices and topological charge -- an explicit example

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore, the time evolution of the vortex line discussed in this work can be viewed as a gif movie, available for download by following the PostScript link below -- watch for the cute feature at the self-intersection poin

Abelian Projection without Ambiguities

f an abelian subgroup U(1) N \Gamma1 of the non-abelian gauge group SU(N) is left unfixed, one obtains an abelian gauge theory whose gauge field content consists of "electrically" charged vector fields and "magnetic" monopoles in addition to the N \Gamma 1 abelian "photons". The magnetic monopoles arise as defects in the gauge fixing. An example of such a partial gauge condition in the continuum is given by the covariant gauge 1) ) X ¯ i @ ¯ \Upsilon iA 3 ¯ j A \Sigma ¯ = 0 : (1 . 1) In this gauge, the non-abelian components A 1;2 are covariantly constant with respect to the abelian subgroup which is taken in the 3-direction. There is no gauge condition on the abelian component A 3 . On the lattice, the most popula