E
                  6
           unification model building. III. Clebsch–Gordan coefficients in E6 tensor products of the 27 with higher dimensional representations

Anderson, Gregory W.; Blažek, T.

doi:10.1063/1.1448134

Cited by 6 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One could have used a completely group theoretical approach as done in Ref. [44], but the oscillator expansion technique is more field theoretical and seems more intuitive to consider the case where the breaking of SO(2N) is done down to SU(N). In addition there are other methods in the literature [45][46][47][48] that can be used for computing the SO(2N) invariant couplings, but we shall not consider these methods in this paper.…”

Section: The So(2n) Spinor Representationmentioning

confidence: 99%

, a C++ library for Yukawa decomposition in SO(2N) models

Cardoso

Emmanuel-Costa

Gonçalves

et al. 2016

Computer Physics Communications

View full text Add to dashboard Cite

We present in this paper the SO Spin library, which calculates an analytic decomposition of the Yukawa interactions invariant under SO(2N) in terms of an SU(N) basis. We make use of the oscillator expansion formalism, where the SO(2N) spinor representations are expressed in terms of creation and annihilation operators of a Grassmann algebra acting on a vacuum state. These noncommutative operators and their products are simulated in SO Spin through the implementation of doubly-linked-list data structures. These data structures were determinant to achieve a higher performance in the simplification of large products of creation and annihilation operators. We illustrate the use of our library with complete examples of how to decompose Yukawa terms invariant under SO(2N) in terms of SU(N) degrees of freedom for N = 2 and 5. We further demonstrate, with an example for SO(4), that higher dimensional field-operator terms can also be processed with our library. Finally, we describe the functions available in SO Spin that are made to simplify the writing of spinors and their interactions specifically for SO(10) models.

show abstract

Section: The So(2n) Spinor Representationmentioning

confidence: 99%

, a C++ library for Yukawa decomposition in SO(2N) models

Cardoso

Emmanuel-Costa

Gonçalves

et al. 2016

Computer Physics Communications

View full text Add to dashboard Cite

show abstract

“…Anderson and Blažek [2][3][4] found certain Clebsch-Gordan coefficients in connection with the E 6 unification model building. Fernández-Núãez, Garcia-Fuertes and Perelomov [14] used the quantum Calogero-Sutherland model corresponding to the root system of E 6 to calculate Clebach-Gordan series for this algebra.…”

Section: Introductionmentioning

confidence: 99%

Polynomial Representation of E6 and Its Combinatorial and PDE Implications

2008

Preprint

View full text Add to dashboard Cite

In this paper, we use partial differential equations to find the decomposition of the polynomial algebra over the basic irreducible module of E 6 into a sum of irreducible submodules. It turns out that the cubic polynomial invariant corresponding to the Dicksons' invariant trilinear form is the unique fundamental invariant. Moreover, we obtain a combinatorial identity saying that the dimensions of certain irreducible modules of E 6 are correlated by the binomial coefficients of twenty-six. Furthermore, we find all the polynomial solutions for the invariant differential operator corresponding to the Dickson trilinear form in terms of the irreducible submodules.

show abstract

“…Five different appendices collect various definitions and technical results. All explicit computation in E 6 has been performed using methods from [21] and [11]; also, [22,23,24] might also prove useful to the reader.…”

Section: Introductionmentioning

confidence: 99%

A Minimal Supersymmetric $\mathrm{E}_6$ Unified Theory

Babu,

Bajc,

Susič

2015

Preprint

View full text Add to dashboard Cite

We show explicitly that supersymmetric E 6 Grand Unified Theory with a Higgs sector consisting of {27 + 27 + 351 + 351 + 78} fields provides a realistic scenario for symmetry breaking and fermion mass generation. While gauge symmetry breaking can be achieved without the 78 field, its presence is critical for a successful doublettriplet mass splitting. The Yukawa sector of the model consists of only two symmetric matrices describing all of quark, lepton and neutrino masses and mixings. The fermion mass matrices are computed at low energy and a fit to the second and third generation masses and mixings is performed. We find a good numerical fit to the low-energy data. Thus, this model, having 11 superpotential parameters, alongside the two symmetric Yukawa matrices, seems to be the best realistic candidate for a minimal renormalizable supersymmetric E 6 unified theory.

show abstract

E 6 unification model building. III. Clebsch–Gordan coefficients in E6 tensor products of the 27 with higher dimensional representations

Cited by 6 publications

References 11 publications

, a C++ library for Yukawa decomposition in SO(2N) models

, a C++ library for Yukawa decomposition in SO(2N) models

Polynomial Representation of E6 and Its Combinatorial and PDE Implications

A Minimal Supersymmetric $\mathrm{E}_6$ Unified Theory

Contact Info

Product

Resources

About