1,071 research outputs found
HyperKhaler Metrics Building and Integrable Models
Methods developed for the analysis of integrable systems are used to study
the problem of hyperK\"ahler metrics building as formulated in D=2 N=4
supersymmetric harmonic superspace. We show, in particular, that the constraint
equation and its
Toda like generalizations are integrable. Explicit solutions together with the
conserved currents generating the symmetry responsible of the integrability of
these equations are given. Other features are also discussedComment: Latex file, 12 page
Four Dimensional Graphene
Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD
given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond
lattice H_4. We first study the link between the H_4 and SU(5); then we refine
the BBTW 4D lattice action by using the weight vectors \lambda_1, \lambda_2,
\lambda_3, \lambda_4, \lambda_5 of the 5-dimensional representation of SU(5)
satisfying {\Sigma}_i\lambda_i=0. After that we study explicitly the solutions
of the zeros of the Dirac operator D in terms of the SU(5) simple roots
\alpha_1, \alpha_2, \alpha_3, \alpha_4 generating H_4; and its fundamental
weights \omega_1, \omega_2, \omega_3, \omega_4 which generate the reciprocal
lattice H_4^\ast. It is shown, amongst others, that these zeros live at the
sites of H_4^\ast; and the continuous limit D is given by ((id\surd5)/2)
\gamma^\muk_\mu with d, \gamma^\mu and k_\mu standing respectively for the
lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector.
Other features such as differences with BBTW model as well as the link between
the Dirac operator following from our construction and the one suggested by
Creutz using quaternions, are also given.
Keywords: Graphene, Lattice QCD, 4D hyperdiamond, BBTW model, SU(5) Symmetry.Comment: LaTex, 26 pages, 1 figure, To appear in Phys Rev
Building SO- models with symmetry
Using characters of finite group representations and monodromy of matter
curves in F-GUT, we complete partial results in literature by building SO models with dihedral discrete symmetry. We first
revisit the -and -models from the discrete
group character view, then we extend the construction to .\ We
find that there are three types of models
depending on the ways the -triplets break down in terms of
irreducible - representations: as
or $\left({\beta}\right) \boldsymbol{\
1}_{_{+,+}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,-}};\left({\gamma}\right) \mathbf{1}_{_{+,-}}\oplus \mathbf{2}_{_{0,0}}$.
Superpotentials and other features are also given.Comment: 20 pages, Nuclear Physics B (2015
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