We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the S...

Anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that anomaly at low energy is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody levels for anomalous discrete family symmetries. As the first example we consider discrete abelian Baryon number and Lepton number symmetries in the minimal supersymm...

We discuss sharpness in the Hausdorff Young theorem for unimodular groups. First the functions on unimodular locally compact groups for which equality holds in the Hausdorff Young theorem are determined. Then it is shown that the Hausdorff Young theorem is not sharp on any unimodular group which contains the real Une as a direct summand, or any unimodular group which contains an Abelian normal ...

A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce two nilpotent Lie algebras and their extended solvable Lie algebras associated with each tree diagram. The solvable tree diagram Lie algebras turn out to be complete Lie algebras of maximal rank analogous to the Borel...

The number of subgroups of type n and cotype v in a finite abelian p-group of type A is a polynomial g$v(p) with integral coefficients. We prove g u v ( p ) has nonnegative coefficients for all partitions p and v if and only if no two parts of A differ by more than one. Necessity follows from a few simple facts about Hall-Littlewood symmetric functions; sufficiency relies on properties of certa...

We extend standard path–integral techniques of bosonization and duality to the setting of noncommutative geometry. We start by constructing the bosonization prescription for a free Dirac fermion living in the noncommutative plane Rθ. We show that in this abelian situation the fermion theory is dual to a noncommutative Wess–Zumino–Witten model. The non–abelian situation is also constructed along...

A path integral description of an effective action of monopoles in Abelian projections of Yang-Mills theories is discussed and used to establish a projection independence of the effective action. A dynamic regime in which the effective dynamics may contain massive solitonic excitations is described. Numerical simulations of lattice Yang-Mills theories show that certain topological defects, whic...

Let A be an abelian variety over the function field K of a compact Riemann surface B. Fix model $$f :{\mathcal {A}} \rightarrow B$$ A/K and effective horizontal divisor $${\mathcal {D}}\subset {\mathcal {A}}$$ . We give sufficient condition on {D}}$$ for finiteness set $$(S, {D}})$$ -integral sections every finite subset $$S \subset These integral $$\sigma $$ are algebraic satisfy geometric ( \...

Representations of the Abelian-projected SU(2)and SU(3)-gluodynamics in terms of the magnetic monopole currents are derived. Besides the quadratic part, the obtained effective actions contain interactions of these currents with the world-sheets of electric strings in 4D or electric vortex lines in 3D. Next, we illustrate that 3D compact QED is a small gauge boson mass limit of 3D Abelian Higgs ...