Related papers: Berenstein-Zelevinsky triangles, elementary coupli…
We compute the representations (``nimreps'') of the fusion algebra of affine sl(N), which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general…
I discuss gauge coupling unification in a class of superstring standard--like models, which are derived in the free fermionic formulation. Recent calculations indicate that the superstring unification scale is at $O(10^{18}GeV)$ while the…
Fermionic artificial matter realized with cold atoms grants access to an unprecedented degree of control on sophisticated many-body effects with an enhanced flexibility of the operating conditions. We consider three-component fermions with…
We continue the study of hidden Z_2 symmetries of the four-point sl(2)_k Knizhnik-Zamolodchikov equation iniciated in hep-th/0508019. Here, we focus our attention on the four-point correlation function in those cases where one spectral…
We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices…
In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to…
Motivated by the Bekenstein Hawking formula and the area law behaviour of entanglement entropy, we propose that in any UV finite theory of quantum gravity with a smooth spacetime, the total entropy for a pure state in a co-dimension one…
Unitarity is a fundamental property of any theory required to ensure we work in a theoretically consistent framework. In comparison with the quark sector, experimental tests of unitarity for the 3x3 neutrino mixing matrix are considerably…
Generalizing the well-known spin-squeezing inequalities, we study the relation between squeezing of collective $N$-particle $su(d)$ operators and many-body entanglement geometry in multi-particle systems. For that aim, we define the set of…
In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…
We discuss the low energy implications of gauge coupling unification at the string scale, taking into account string threshold corrections in the $SU(4) {\times} O(4)$ model. We express $sin^2\theta_W$ and $a_3$ as functions of the…
We compute, by free field techniques, the scalar product of the SU(2) Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional integral over positions of ``screening charges'' and one complex modular parameter. It uses…
We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it…
The radiative electroweak symmetry breaking, the unification of third-generation Yukawa couplings, and flavor-changing rare decay are investigated in two types of supersymmetric SO(10) scenarios taking into account of the effects of…
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the…
Taking into account the $SU(3)_f$ breaking effects, the strong coupling constants of the $\pi$, $K$ and $\eta$ mesons with decuplet baryons are calculated within light cone QCD sum rules method. It is shown that all coupling constants, even…
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits (Phys. Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher dimension. The spirit…
A neutrino mass model is suggested within an $SU(4)\times U(1)$ -- electroweak theory. The smallness of neutrino masses can be guaranteed by a seesaw mechanism realized through Yukawa couplings to a scalar $SU(4)$-decuplet. In this scheme…
This paper provides a non-standard analogue of Bezout's theorem. This is acheived by showing that, in all characteristics, the notion of Zariski multiplicity coincides with intersection multiplicity when we consider the full families of…
An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single particle states is presented. An interesting geometric structure of fermionic entanglement is…