Non-abelian Fundamental Group Research Articles

Phenomenological studies of rank-5 Calabi-Yau models

We study the phenomenology of heterotic superstring models compactified on Calabi-Yau manifolds with non-abelian fundamental groups which can yield the rank-5 gauge group SU(3) c × SU(2) L × U(1) 2 in four dimensions. We examine one 2-generation model and several 4-generation models. They all have fatal problems with proton decay and/or neutrino masses. The most interesting 4-generation model avoids rapid proton decay at the expense of a neutrino weighing more than the proton and an unrealistic pattern of Cabibbo mixing.

New manifolds for superstring compactification

We construct new manifolds with SU(3) holonomy that are candidate vacua for superstring theory and give a detailed explanation of the techniques involved. Some of these manifolds have a non-abelian fundamental group and thus can lead to a rank five low energy gauge group. Models with an odd number of generations are obtained.CP violation is discussed in this context and shown to occur generically. Topological features of the Yukawa couplings are also discussed.

A spin model with non-abelian Π 1

A spin model in two space dimensions with non-abelian fundamental topological group ( Π 1 = Q) is studied. The model has non-abelian vortices which change their relative sign when crossing each other. The phase structure of the model related to the presence of non-abelian vortices and their global symmetries is studied.

Some examples of compact supermanifolds with non-Abelian fundamental group

A detailed construction is given of a supermanifold which is compact and has far from trivial topology. Higher dimensional examples are also described. The Grassmann algebra from which the supermanifolds are constructed may have finite or infinite dimension.

Flux metamorphosis

Some consequences of a non-abelian fundamental group π 1(G/H) are investigated in the context of spontaneously broken gauge theories. Vortices associated with elements of π 1(G/H) which do not commute cannot pass through each other, without remaining attached. Various simple models featuring this phenomenon are presented. A rather general method for generating the relevant ansätze for the fields is given as well.

Some plane curves whose complements have non-abelian fundamental groups

Some plane curves whose complements have non-abelian fundamental groups