Related papers: A construction for R-matrices without difference p…
A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the…
The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering…
In the framework of quantum groups and additive R-matrices, the fusion procedure allows to construct higher-dimensional solutions of the Yang-Baxter equation. These solutions lead to integrable one-dimensional spin-chain Hamiltonians. Here…
We consider the most general class possible of soft supersymmetry breaking terms that can be added to the MSSM, with and without R-parity violation, consistent with the sole requirement that no quadratic divergences are induced. We…
The messenger sector of existing models of gauge-mediated supersymmetry breaking may be simplified by using a non-renormalizable superpotential term to couple the vector-like quark and lepton messenger fields to a chiral gauge-invariant of…
We introduce a simple method to extract the representation content of the spectrum of a system with SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4) symmetry, such as conformal field…
An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…
We consider nonnegative r-potent matrices with finite dimensions and study their decomposability. We derive the precise conditions under which an r-potent matrix is decomposable. We further determine a general structure for the r-potent…
We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved…
We study in detail the particle spectrum in anomaly mediated supersymmetry breaking models in which supersymmetry breaking terms are induced by the super-Weyl anomaly. We investigate the minimal anomaly mediated supersymmetry breaking…
We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that…
We find new families of solutions of the $D_{n+1}^{(2)}$ boundary Yang-Baxter equation. The open spin-chain transfer matrices constructed with these K-matrices have quantum group symmetry corresponding to removing one node from the…
We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$…
Let g be a complex semisimple Lie algebra and Yg its Yangian. Drinfeld proved that the universal R-matrix of Yg gives rise to rational solutions of the quantum Yang-Baxter equations on irreducible, finite-dimensional representations of Yg.…
We discuss local \R-symmetry as a potentially powerful new model building tool. We first review and clarify that a $U(1)$ \R-symmetry can only be gauged in local and not in global supersymmetry. We determine the anomaly-cancellation…
The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…
The simplest unified extension of the Minimal Supersymmetric Standard Model with bilinear R-Parity violation provides a predictive scheme for neutrino masses which can account for the observed atmospheric and solar neutrino anomalies.…
We show that a supersymmetric standard model exhibiting anomaly mediated supersymmetry breaking can generate naturally the observed neutrino mass spectrum as well mixings when we include bilinear R-parity violation interactions. In this…
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an integrable case of the H\'enon-Heiles…
We study neutrino masses and mixing in Supersymmetric Models without $R$ parity and with generic soft Supersymmetry breaking terms. Neutrinos acquire mass from various sources: tree level neutrino--neutralino mixing, loop effects and…