Related papers: The Mathematical Structure of $U$-Spin Amplitude S…
It is shown that in supersymmetric SU(N) models with N>5 the so-called doubly lopsided mass matrix structure can emerge in a natural way. The non-trivial flavor structure is entirely accounted for by the SU(N) gauge symmetry and…
In Variational Analysis, VU-theory provides a set of tools that is helpful for understanding and exploiting the structure of nonsmooth functions. The theory takes advantage of the fact that at any point, the space can be separated into two…
We develop a simple computational tool for $SU(3)$ analogous to Bargmann's calculus for $SU(2)$. Crucial new inputs are, (i) explicit representation of the Gelfand-Zetlin basis in terms of polynomials in four variables and positive or…
We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent…
In the framework of generalized Oppenheim expansions we prove strong law of large numbers for lightly trimmed sums. In the first part of this work we identify a particular class of expansions for which we provide a convergence result…
We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and…
The supersymmetric standard model with supergravity-inspired soft breaking terms predicts a rich pectrum of sparticles to be discovered at the SSC, LHC and NLC. Because there are more supersymmetric particles than unknown parameters, one…
In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as "Birch sums". Our main theorem gives upper and lower bounds (of nearly the same order of magnitude) for the…
A four-term recurrence relation for squared spherical Bessel functions is shown to yield closed-form expressions for several types of finite weighted sums of these functions. The resulting sum rules, which may contain an arbitrarily large…
Sum rules among superparticle masses are derived under the assumption that models beyond the MSSM are four-dimensional supersymmetric grand unified theories or five-dimensional supersymmetric orbifold grand unified theories. Sfermion sum…
Requiring the soft supersymmetry-breaking (SSB) parameters in finite gauge-Yukawa unified models to be finite up to and including two-loop order, we derive a two-loop sum rule for the soft scalar-masses. It is shown that this sum rule…
Charge sum rules for quark fragmentation functions are studied. The simultaneous implementation of the conservation of electric and baryon charges, strangeness and isospin symmetry is achieved when the fragmentation to both mesons and…
We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one…
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…
The multiplicities of the decomposition of the product of an arbitrary number $n$ of spin $s$ states into irreducible $SU(2)$ representations are computed. Two complementary methods are presented, one based on random walks in representation…
We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule, with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an…
It is shown that a certain sum rule for soft supersymmetry-breaking scalar masses, which has been recently found in a certain class of superstring models, is universal for gauge-Yukawa unified models. To explain this coincidence, we argue…
We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…
The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their characters involve divergent sums over spins. We propose a suitable…
We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D $\mathcal{N}=4$ SYM, and therefore we consider a 6D Grassmannian formula, where we can…