Ampleness in the free group

We show that the theory of the free group -- and more generally the theory of any torsion-free hyperbolic group -- is $n$-ample for any $n\geq 1$. We give also an explicit description of the imaginary algebraic closure in free groups

Path Integral Bosonization of Massive GNO Fermions

We show the quantum equivalence between certain symmetric space sine-Gordon models and the massive free fermions. In the massless limit, these fermions reduce to the free fermions introduced by Goddard, Nahm and Olive (GNO) in association with symmetric spaces $K/G$. A path integral formulation is given in terms of the Wess-Zumino-Witten action where the field variable $g$ takes value in the orthogonal, unitary, and symplectic representations of the group $G$ in the basis of the symmetric space. We show that, for example, such a path integral bosonization is possible when the symmetric spaces $K/G$ are $SU(N) \times SU(N)/SU(N); N \le 3, ~ Sp(2)/U(2)$ or $SO(8)/U(4)$. We also address the relation between massive GNO fermions and the nonabelian solitons, and explain the restriction imposed on the fermion mass matrix due to the integrability of the bosonic model.Comment: 11 page

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physic

Nonabelian Vortices on Surfaces and Their Statistics

We discuss the physics of topological vortices moving on an arbitrary surface M in a Yang-Mills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or nonorientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is nonabelian.Comment: 27 pages, 6 figures, requires harvma

Explicit Constructions of Quasi-Uniform Codes from Groups

We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian groups. Potentials applications comprise the design of almost affine codes and non-linear network codes