Related papers: Berenstein-Zelevinsky triangles, elementary coupli…
We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The…
In a generic Grand Unified Theory with a relatively small dispersion of the spectrum around the $Z$-boson and the unification masses, a connection is established, exact at one loop level, between $M_Z$, $G_{\rm F}$, $\alpha(M_Z)$ and the…
The periodic Temperley-Lieb category consists of connectivity diagrams drawn on a ring with $N$ and $N'$ nodes on the outer and inner boundary, respectively. We consider families of modules, namely sequences of modules $\mathsf{M}(N)$ over…
The condition of unification of gauge couplings in the minimal supersymmetric standard model provides successful predictions for the weak mixing angle as a function of the strong gauge coupling and the supersymmetric threshold scale. In…
Singular values are used to construct physically admissible 3-dimensional mixing matrices characterized as contractions. Depending on the number of singular values strictly less than one, the space of the 3-dimensional mixing matrices can…
Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local…
Let $\nu$ be either the Ozsv\'ath-Szab\'o $\tau$-invariant or the Rasmussen $s$-invariant, suitably normalized. For a knot $K$, Livingston and Naik defined the invariant $t_\nu(K)$ to be the minimum of $k$ for which $\nu$ of the $k$-twisted…
We show that all mixing angles are determined, within experimental uncertainty, by a product of SU(2) horizontal symmetries intimately linked to the algebra of weak neutral currents. This concerns: on one hand, the three quark mixing…
We reanalyze precision LEP data and coupling constant unification in the minimal supersymmetric $SU(5)$ model including the evolution of the gaugino masses. We derive general bounds on the primordial gaugino supersymmetry-breaking…
In the minimal supersymmetric standard model, the three gauge couplings appear to unify at a mass scale near $2 \times 10^{16}$ GeV. We investigate the possibility that intermediate scale particle thresholds modify the running couplings so…
We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on…
A realistic SU(3)_C x SU(3)_W unified theory is constructed with a TeV sized extra dimension compactified on the orbifold S_1/Z_2, leaving only the standard model gauge group SU(3)_C x SU(2)_L x U(1)_Y unbroken in the low energy 4D theory.…
In scenarios with the fundamental unification scale at the TeV one expects string excitations of the standard model fields at accessible energies. We study the neutrino-nucleon cross section in these models. We show that duality of the…
Fusion rules for Wess-Zumino-Witten (WZW) models at fractional level can be defined in two ways, with distinct results. The Verlinde formula yields fusion coefficients that can be negative. These signs cancel in coset fusion rules, however.…
We calculate the tunneling conductance spectra of a normal metal / insulator / triplet superconductor from the reflection amplitudes using the Blonder-Tinkham-Klapwijk (BTK) formula. For the triplet superconductor we assume one special…
We study the classical limit of a tensor product of Kirillov-Reshetikhin modules over a quantum loop algebra, and show that it is realized from the classical limits of the tensor factors using the notion of fusion products. In the process…
The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…
Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D sine-Gordon model, plays an important role in the low dimensional physics. We relate the operator content of the BKT transition to that of the SU(2)…
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…
The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…