Topological Symmetries

We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and (2,1). This leads to a novel derivation of the algebras of supersymmetry and $p=2$ parasupersummetry.Comment: Plain LaTeX Ref: Mod. Phys. Lett. A 15, 175-184 (2000

Low energy fixed points of the sigma-tau and the O(3) symmetric Anderson models

We study the single channel (compactified) models, the sigma-tau model and the O(3) symmetric Anderson model, which were introduced by Coleman et al., and Coleman and Schofield, as a simplified way to understand the low energy behaviour of the isotropic and anisotropic two channel Kondo systems. These models display both Fermi liquid and marginal Fermi liquid behaviour and an understanding of the nature of their low energy fixed points may give some general insights into the low energy behaviour of other strongly correlated systems. We calculate the excitation spectrum at the non-Fermi liquid fixed point of the sigma-tau model using conformal field theory, and show that the results are in agreement with those obtained in recent numerical renormalization group (NRG) calculations. For the O(3) Anderson model we find further logarithmic corrections in the weak coupling perturbation expansion to those obtained in earlier calculations, such that the renormalized interaction term now becomes marginally stable rather than marginally unstable. We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak and strong coupling regimes and show that the chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations.Comment: 23 pages, LaTeX, 11 figures includes as eps-files, submitted to Phys. Rev.

Solitons in the Higgs phase -- the moduli matrix approach --

We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories. We characterize the total moduli space of these elementary as well as composite solitons. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices, and walls. Review parts contain our works on domain walls (hep-th/0404198, hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices (hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135, hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129, hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective Lagrangian on walls and vortices (hep-th/0602289), classification of BPS equations (hep-th/0506257), and Skyrmions (hep-th/0508130).Comment: 89 pages, 33 figures, invited review article to Journal of Physics A: Mathematical and General, v3: typos corrected, references added, the published versio

The target space geometry of N=(2,1) string theory

We describe the ${\cal{O}}({\alpha'}^0)$ constraints on the target space geometry of the $N=(2,1)$ heterotic superstring due to the left-moving $N=1$ supersymmetry and $U(1)$ currents. In the fermionic description of the internal sector supersymmetry is realized quantum mechanically, so that both tree-level and one-loop effects contribute to the order ${\cal{O}}({\alpha'}^0)$ constraints. We also discuss the physical interpretation of the resulting target space geometry in terms of configurations of a $2+2$-dimensional object propagating in a $10+2$-dimensional spacetime with a null isometry, which has recently been suggested as a unified description of string and M theory.Comment: 41 pages, 5 figures, standard LaTeX, uses epsf.tex. Some typos corrected, discussion in footnote 1 correcte

Quantum Mechanical Symmetries and Topological Invariants

We give the definition and explore the algebraic structure of a class of quantum symmetries, called topological symmetries, which are generalizations of supersymmetry in the sense that they involve topological invariants similar to the Witten index. A topological symmetry (TS) is specified by an integer n>1, which determines its grading properties, and an n-tuple of positive integers (m_1,m_2,...,m_n). We identify the algebras of supersymmetry, p=2 parasupersymmetry, and fractional supersymmetry of order n with those of the Z_2-graded TS of type (1,1), Z_2-graded TS of type (2,1), and Z_n-graded TS of type (1,1,...,1), respectively. We also comment on the mathematical interpretation of the topological invariants associated with the Z_n-graded TS of type (1,1,...,1). For n=2, the invariant is the Witten index which can be identified with the analytic index of a Fredholm operator. For n>2, there are n independent integer-valued invariants. These can be related to differences of the dimension of the kernels of various products of n operators satisfying certain conditions.Comment: Revised version, to appear in Nucl. Phys.

Polarization and magnetization dynamics of a field-driven multiferroic structure

We consider a multiferroic chain with a linear magnetoelectric coupling induced by the electrostatic screening at the ferroelectric/ferromagnet interface. We study theoretically the dynamic ferroelectric and magnetic response to external magnetic and electric fields by utilizing an approach based on coupled Landau- Khalatnikov and finite-temperature Landau-Lifshitz-Gilbert equations. Additionally, we compare with Monte Carlo calculations. It is demonstrated that for material parameters corresponding to BaTiO3/Fe the polarization and the magnetization are controllable by external magnetic and electric fields respectively

Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N=2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (non-equivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras, and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multi-fermion systems.Comment: 20 pages, to appear in J.Phys.

Irrational Conformal Field Theory

This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational conformal field theory. Discussion of the dynamics includes the generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding heat-like systems on the torus and the generic world- sheet action of irrational conformal field theory.Comment: 195 pages, Latex, 12 figures, to appear in Physics Reports. Typos corrected in Sections 13 and 14, and a footnote added in Section 1

Determination of the prebiotic activity of wheat arabinogalactan peptide (AGP) using batch culture fermentation

Purpose To test the prebiotic activity of wheat arabinogalactan-peptide (AGP), which is a soluble dietary fibre composed of arabinogalactan polysaccharide linked to a 15-residue peptide, which accounts for up to 0.4% of the dry weight of wheat flour. Methods The prebiotic activity of AGP prepared from white wheat flour was tested using in-vitro fermentation by colonic bacteria in automated pH controlled anaerobic stirred batch cultures and compared to fructooligosaccharide (FOS) and wheat flour arabinoxylan (AX). Bacterial populations were measured using fluorescence in-situ hybridisation (flow-FISH) and short-chain fatty acid (SCFA) concentrations were measured using HPLC. Results Fermentation of AGP resulted in a significant bifidogenic activity and increased concentrations of SCFAs, mainly acetate after 24 h of fermentation. Conclusions These results were comparable to those obtained with AX and confirm the prebiotic potential of AGP. Furthermore, fermentation of a mixture of AGP and AX was faster compared to the single substrates and more similar to FOS, indicating that combinations of fermentable carbohydrates with different structures are potentially more effective as prebiotics than single substrates