Related papers: On an SO(5) unification attempt for the cuprates
The generalization of multiplicative unitary notion from compact quantum groups to compact quantum semigroups is considered. We show why the same construction doesn't work in this case by giving examples of C*-algebras with non-trivial…
Let $\Goo$ be a semisimple real Lie group with unitary dual $\Ghat$. The goal of this note is to produce new upper bounds for the multiplicities with which representations $\pi \in \Ghat$ of cohomological type appear in certain spaces of…
We investigate the unification constraints in the minimal sypersymmetric grand unified theories based on SU(5) gauge symmetry. The most general constraints on the spectrum of minimal supersymmetric SU(5) and flipped SU(5) are shown. The…
A multiparameter class of integrable systems is introduced.
In F-theory GUT constructions Yukawa couplings necessarily take place at the intersection of three matter curves. For generic geometric configurations this gives rise to problematic Yukawa couplings unable to reproduce the observed…
Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification…
In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend his proof to some semi-convex energies provided the curvature…
Asymptotic grand unification provides an alternative approach to gradually unify gauge couplings in the UV limit, where they reach a non-trivial UV fixed point. Using an economical and realistic particle content setup, we demonstrate that…
We recall the classification of the irreducible representations of $SL(2)_q$, and then give fusion rules for these representations. We also consider the problem of $\cR$-matrices, intertwiners of the differently ordered tensor products of…
We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…
It is often argued that in the class of non-supersymmetric SO(10) grand unified theories there is barely any room for reconciling the lower bound on the position of the GUT scale emerging from the proton decay searches and the lower limit…
We investigate supersymmetric SU(5) grand-unified theories (GUTs) realized in 5 space-time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S^1/(Z_2 x Z_2') orbifold with two 3-branes. The doublet-triplet…
This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…
We introduce the notion of soficity for locally compact groups and list a number of open problems.
I comment on two recent papers on Kerr effect as evidence of gyrotropic order in cuprates, and I suggest that the arguments may not be sound. The difficulty is that in practically all cases the wave vector $k_{z}$ perpendicular to the…
Grand unified models in four dimensions typically suffer from the doublet-triplet splitting problem. This obstacle can be overcome in higher-dimensional settings, where a non-trivial gauge group topography can explain the simultaneous…
We suggest SU(5)$'$ in the hidden sector toward a possible gauge mediated supersymmetry breaking scenario for removing the SUSY flavor problem, with an example constructed in $\Z_{12-I}$ with three families. The example we present has the…
This dissertation collects together results on Patience Sorting and its generalizations. It incorporates the results of math.CO/0506358, math.CO/0507031, and math.CO/0512122, as well as previously unpublished results.
I review our recent attempts toward obtaining the MSSM from string orbifold compactification. The required constraints are the existence of three families and R parity, vectorlike exotics, one pair of Higgs doublets, and the SU(5)$'$ hidden…
We analyze the gauge unification in minimal supersymmetric SO(10) grand unified theories in 5 dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam…