5 research outputs found
Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system framework
Using a generalized procedure for obtaining the dispersion relation and the
equation of motion for a propagating fermionic particle, we examine previous
claims for a preferred axis at (), embedded
in the framework of very special relativity (VSR). We show that, in a
relatively high energy scale, the corresponding equation of motion is reduced
to a conserving lepton number chiral equation previously predicted in the
literature. Otherwise, in a relatively low energy scale, the equation is
reduced to the usual Dirac equation for a free propagating fermionic particle.
It is accomplished by the suggestive analysis of some special cases where a
nonlinear modification of the action of the Lorentz group is generated by the
addition of a modified conformal transformation which, meanwhile, preserves the
structure of the ordinary Lorentz algebra in a very peculiar way. Some feasible
experiments, for which Lorentz violating effects here pointed out may be
detectable, are suggested.Comment: 10 page
Deforming the Maxwell-Sim Algebra
The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in
which the momentum generators no longer commute, but satisfy
. The charges commute with the momenta,
and transform tensorially under the action of the angular momentum generators.
If one constructs an action for a massive particle, invariant under these
symmetries, one finds that it satisfies the equations of motion of a charged
particle interacting with a constant electromagnetic field via the Lorentz
force. In this paper, we explore the analogous constructions where one starts
instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra
of Very Special Relativity. It admits an analogous non-central extension, and
we find that a particle action invariant under this Maxwell-Sim algebra again
describes a particle subject to the ordinary Lorentz force. One can also deform
the ISim algebra to DISim, where is a non-trivial dimensionless
parameter. We find that the motion described by an action invariant under the
corresponding Maxwell-DISim algebra is that of a particle interacting via a
Finslerian modification of the Lorentz force.Comment: Appendix on Lifshitz and Schrodinger algebras adde
Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
In this paper, we look for metrics of cohomogeneity one in D=8 and D=7
dimensions with Spin(7) and G_2 holonomy respectively. In D=8, we first
consider the case of principal orbits that are S^7, viewed as an S^3 bundle
over S^4 with triaxial squashing of the S^3 fibres. This gives a more general
system of first-order equations for Spin(7) holonomy than has been solved
previously. Using numerical methods, we establish the existence of new
non-singular asymptotically locally conical (ALC) Spin(7) metrics on line
bundles over \CP^3, with a non-trivial parameter that characterises the
homogeneous squashing of CP^3. We then consider the case where the principal
orbits are the Aloff-Wallach spaces N(k,\ell)=SU(3)/U(1), where the integers k
and \ell characterise the embedding of U(1). We find new ALC and AC metrics of
Spin(7) holonomy, as solutions of the first-order equations that we obtained
previously in hep-th/0102185. These include certain explicit ALC metrics for
all N(k,\ell), and numerical and perturbative results for ALC families with AC
limits. We then study D=7 metrics of holonomy, and find new explicit
examples, which, however, are singular, where the principal orbits are the flag
manifold SU(3)/(U(1)\times U(1)). We also obtain numerical results for new
non-singular metrics with principal orbits that are S^3\times S^3. Additional
topics include a detailed and explicit discussion of the Einstein metrics on
N(k,\ell), and an explicit parameterisation of SU(3).Comment: Latex, 60 pages, references added, formulae corrected and additional
discussion on the asymptotic flow of N(k,l) cases adde
A New Fractional D2-brane, G_2 Holonomy and T-duality
Recently, a new example of a complete non-compact Ricci-flat metric of G_2
holonomy was constructed, which has an asymptotically locally conical structure
at infinity with a circular direction whose radius stabilises. In this paper we
find a regular harmonic 3-form in this metric, which we then use in order to
obtain an explicit solution for a fractional D2-brane configuration. By
performing a T-duality transformation on the stabilised circle, we obtain the
type IIB description of the fractional brane, which now corresponds to D3-brane
with one of its world-volume directions wrapped around the circle.Comment: Latex, 13 page