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Register a new user5-Dimensional $SO(1, 4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
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In this paper we discuss how the Magueijo-Smolin Doubly Special Relativity proposal may obtained from a singular Lagrangian action. The deformed energy-momentum dispersion relation rises as a particular gauge, whose covariance imposes the non-linear Lorentz group action. Moreover, the additional invariant scale is present from the beginning as a coupling constant to a gauge auxiliary variable. The geometrical meaning of the gauge fixing procedure and its connection to the free relativistic particle are also described.
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We discuss a way to obtain the doubly special relativity kinematical rules (the deformed energy-momentum relation and the nonlinear Lorentz transformations of momenta) starting from a singular Lagrangian action of a particle with linearly realized SO(1,4) symmetry group. The deformed energy-momentum relation appears in a special gauge of the model. The nonlinear transformations of momenta arise from the requirement of covariance of the chosen gauge.
We show that depending on the direction of deformation of $kappa$-Poincare algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form of de Sitter, anti-de Sitter, and flat space, respectively.
We construct a new SO(3)$times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear uplift formulae for the metric and the 3-form potential. The latter are crucial as this solution appears to be inaccessible to traditional techniques of solving Einsteins field equations, and is arguably the most complicated closed form solution of this type ever found. The solution is also a promising candidate for a stable non-supersymmetric solution of M-theory uplifted from gauged supergravity. The technique that we present here may be applied more generally to uplift other solutions of gauged supergravity.
The current status of Doubly Special Relativity research program is shortly presented. I dedicate this paper to my teacher and friend Professor Jerzy Lukierski on occasion of his seventieth birthday.
In the decomposition of $SO(10)$ grand unification to $SU(5) times U(1)_chi$, two desirable features are obtained with the addition of one colored fermion octet $Omega$, one electroweak fermion triplet $Sigma$ and one complex scalar triplet $S$ to the particle content of the standard model with two Higgs doublets. They are (1) gauge coupling unification of $SU(3)_C times SU(2)_L times U(1)_Y$ to $SU(5)$, and (2) the automatic (predestined) emergence of dark matter, i.e. $Omega$, $Sigma$ and $S$, with dark parity given by $(-1)^{Q_chi + 2j}$. It suggests that $U(1)_chi$ may well be the underlying symmetry of the dark sector.
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