The gluon propagator in lattice landau gauge with twisted boundary conditions

We investigate the infrared behaviour of the gluon propagator in Landau gauge on a lattice with twisted boundary conditions. Analytic calculations using Dyson-Schwinger equations, exact renormalization group and stochastic quantization show that the gluon propagator in Landau gauge approaches zero for small momentum. On the other hand lattice calculations and calculations on a four-torus seem to give rise to a non-zero limit. One possible reason for this difference is the existence of zero-momentum fluctuation modes which potentially give a massive contribution to the gluon propagator. Our simulations show that with twisted boundary conditions these zero-momentum modes are suppressed and the gluon propagator becomes smaller than in a periodic ensemble.Torsten Tok, Kurt Langfeld, Hugo Reinhardt, Lorenz von Smeka

A toy model of (grand) unified monopoles

We explore the old idea that, in a theory containing several gauge groups, the topological defects of one gauge group coincide with those of another gauge group. This simple 'unification' constraint has deep consequences, the best known of which is a natural explanation of the fractional electric charge of quarks. Here we explore the consequences of this idea for the phase diagram, in a toy model U(1)x U(1).Comment: PoS(LAT2005)314, 6 pages, 3 figures, for the proceedings of 'Lattice 2005 (Topology and Confinement).

Exact solutions in Einstein-Yang-Mills-Dirac systems

We present exact solutions in Einstein-Yang-Mills-Dirac theories with gauge groups SU(2) and SU(4) in Robertson-Walker space-time $R \times S^3$, which are symmetric under the action of the group SO(4) of spatial rotations. Our approach is based on the dimensional reduction method for gauge and gravitational fields and relates symmetric solutions in EYMD theory to certain solutions of an effective dynamical system. We interpret our solutions as cosmological solutions with an oscillating Yang-Mills field passing between topologically distinct vacua. The explicit form of the solution for spinor field shows that its energy changes the sign during the evolution of the Yang-Mills field from one vacuum to the other, which can be considered as production or annihilation of fermions. Among the obtained solutions there is also a static sphaleron-like solution, which is a cosmological analogue of the first Bartnik-McKinnon solution in the presence of fermions.Comment: 18 pages, LaTeX 2

A certain class of Einstein-Yang-Mills--systems

A class of $G$-invariant Einstein-Yang-Mills (EYM) systems with cosmological constant on homogeneous spaces $G / H$, where $G$ is a semisimple compact Lie group, is presented. These EYM--systems can be obtained in terms of dimensional reduction of pure gravity. If $G / H$ is a symmetric space, the EYM--system on $G / H$ provides a static solution of the EYM--equations on spacetime ${\Bbb R} \times G / H$. This way, in particular, a solution for an arbitrary Lie group $F$, considered as a symmetric space, is obtained. This solution is discussed in detail for the case $F = SU(2)$. A known analytical EYM--system on ${\Bbb R} \times S^3$ is recovered and it is shown - using a relation to the BPST instanton - that this solution is of sphaleron type. Finally, a relation to the distance of Bures and to parallel transport along mixed states is shown.Comment: 16 pages, LaTeX 2