A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological charge is explicitly found. They appear to be identical as the so-called eikonal knots. The relation between energy and topological charge of the solution is a...

A combinatorial formula to generate U (N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of ...

We give a brief overview on interacting symmetry-protected topological (SPT) phases. In particular, we will focus on various cases where the classification of non-interacting fermionic systems breaks down in the presence of interactions. The examples include topological (and trivial) superconductors in one, two and three spatial dimensions, protected by various symmetries such as time-reversal,...

Two distinct methods for measuring topological charge in a nonabelian anyonic system have been discussed in the literature: projective measurement of a single point-like quasiparticle and interferometric measurement of the total topological charge of a group of quasiparticles. Projective measurement by definition is only applied near a point and will project to a topological charge sector near ...

This is a brief review on the work done recently. It is shown that the global constraints of Gauss’ law ensure that the vacuum angle must be quantized in gauge theories with magnetic monopoles. Our quantization rule is given as θ = 0, or θ = 2πN/n (n 6= 0) with integer n being the relevant topological charge of the magnetic monopole and N is an unfixed integer in this approach. This theoretical...

We extend the definition of the topological charge pertaining to the CP (i.e. O(3)) Skyrme-Fadde’ev Hopfion on IR, to candidates for topological charges of CP sigma models on IR, for all n. For this, the Abelian composite connections of the CP sigma models are employed. In higher dimensions (n ≥ 1) it turns out that such charges, described by the nonAbelian composite connections of suitable Gra...

We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol’nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the supersymmetric case, we also show that, in spacetime dimensions greater than two, theories with topological charges necessarily exhibit extended supersymmetry...

A combinatorial formula to generate U (N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of ...

I readdress the issue whether the topological charge of the gauge background has an influence on a hadronic observable. To this end pion correlators in the Schwinger model with 2 dynamical flavours are determined on subensembles with a fixed topological charge. It turns out that the answer depends on a specific function of the sea-quark mass and the box volume which is in close analogy to the L...

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