We consider acyclic groups of low dimension. To indicate our results simply, let G′ be the nontrivial perfect commutator subgroup of a finitely presentable group G. Then def(G) ≤ 1. When def(G) = 1, G′ is acyclic provided that it has no integral homology in dimensions above 2 (a sufficient condition for this is that G′ be finitely generated); moreover, G/G′ is then Z or Z. Natural examples are ...

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter ...

We analyze the possibility of universality violation in diagonal leptonic decays of the Z boson, in the context of interfamily ”see-saw” models. In a minimal extension of the Standard Model with right-handed neutrino fields, we find that universality-breaking effects increase quadratically with the heavy Majorana neutrino mass and may be observed in the running LEP experiments. PACS numbers: 12...

In the presence of a strong magnetic field and under conditions as realized in the crust and the superfluid core of neutron stars, the Hall drift dominates the field evolution. We show by a linear analysis that, for a sufficiently strong large-scale background field depending at least quadratically on position in a plane conducting slab, an instability occurs which rapidly generates small-scale...

Sum-frequency generation in isotropic media is in the electric-dipole approximation the only symmetry allowed for chiral systems. We demonstrate that the sum-frequency intensity from an optically active liquid depends quadratically on the difference in concentration of the two enantiomers. The dominant contribution to the signal is found to be due to the chirality specific electric-dipolar thre...

Quantum corrections to the conductivity of fermion–gauge field models: Application to half filled Landau level and high-T c superconductors. Abstract We calculate the Altshuler-Aronov type quantum correction to the conductivity of 2d charge carriers in a random potential (or random magnetic field) coupled to a transverse gauge field. The gauge fields considered simulate the effect of the Coulom...

The colorful Carathéodory theorem asserts that if X1, X2, . . . , Xd+1 are sets in R, each containing the origin 0 in its convex hull, then exists a set S ⊆ X1 ∪ · · · ∪ Xd+1 with |S ∩ Xi| = 1 for all i = 1, 2, . . . , d + 1 and 0 ∈ conv(S) (we call conv(S) a colorful covering simplex). Deza, Huang, Stephen and Terlaky proved that if the Xi are in general position with respect to 0 (consequentl...

We study dimensional reduction of M5 branes on a circle bundle when the supersymmetry parameter is not constant along circle. When gauge group Abelian and fields appear quadratically in Lagrangian, we can always obtain supersymmetric five-dimensional theory by keeping fermionic nonzero modes that match with corresponding parameter, zero for bosonic as usual. But non-Abelian generalization be fo...

Two ways of describing a group are considered. 1. A group is finiteautomaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasi-finitely axiomatizable if there is a description consisting of a single first-order senten...

A logic of orthogonality characterizes all “orthogonality consequences” of a given class Σ of morphisms, i.e. those morphisms s such that every object orthogonal to Σ is also orthogonal to s. A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes Σ of...