Gauge Theories with a Layered Phase

We study abelian gauge theories with anisotropic couplings in $4+D$ dimensions. A layered phase is present, in the absence as well as in the presence of fermions. A line of second order transitions separates the layered from the Coulomb phase, if $D\leq 3$.Comment: 17 pages+9 figures (in LATeX and PostScript in a uuencoded, compressed tar file appended at the end of the LATeX file) , CPT-94/P.303

Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions

We study a multigrid method for nonabelian lattice gauge theory, the time slice blocking, in two and four dimensions. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method. This result is in accordance with theoretical arguments based on the analysis of the scale dependence of acceptance rates for nonlocal Metropolis updates. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint MS-TPI-94-

Effective Field Theories

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically,the idea is to integrate out the high frequency components of fields. This requires the choice of a "blockspin",i.e. the specification of a low frequency field as a function of the fundamental fields. These blockspins will be the fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspins in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels \A from coarse to fine grid in addition to the averaging kernels $C$ which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The constraint effective potential) is of particular interest. In a Higgs model it yields the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data.Comment: 45 pages, 9 figs., preprint DESY 92-070 (figs. 3-9 added in ps format

Chiral symmetry breakdown:III. Delbourgo’s gauge technique

The quark propagator in massless quantum chromodynamics (QCD) is analyzed using the gauge technique. In both the Feynman and Landau gauges with a Pauli–Villars cutoff, a chirally symmetric solution is found, while a nonsymmetric solution appears at a critical coupling λc>0. As the cutoff is removed, λc tends to 0 but the nonsymmetric solution vanishes in the continuum limit, so that chiral symmetry is then restored

New distal marker closely linked to the fragile X locus

We have isolated II-10, a new X-chromosomal probe that identifies a highly informative two-allele TaqI restriction fragment length polymorphism at locus DXS466. Using somatic cell hybrids containing distinct portions of the long arm of the X chromosome, we could localize DXS466 between DXS296 and DXS304, both of which are closely linked distal markers for fragile X. This regional localization was supported by the analysis, in fragile X families, of recombination events between these three loci, the fragile X locus and locus DXS52, the latter being located at a more distal position. DXS466 is closely linked to the fragile X locus with a peak lod score of 7.79 at a recombination fraction of 0.02. Heterozygosity of DXS466 is approximately 50%. Its close proximity and relatively high informativity make DXS466 a valuable new diagnostic DNA marker for fragile X