239 research outputs found
On generalized Melvin solution for the Lie algebra
A multidimensional generalization of Melvin's solution for an arbitrary
simple Lie algebra is considered. The gravitational model in
dimensions, , contains 2-forms and scalar fields,
where is the rank of . The solution is governed by a set of
functions obeying ordinary differential equations with certain
boundary conditions imposed. It was conjectured earlier that these functions
should be polynomials (the so-called fluxbrane polynomials). The polynomials
, , for the Lie algebra are obtained and a
corresponding solution for is presented. The polynomials depend
upon integration constants , . They obey symmetry and
duality identities. The latter ones are used in deriving asymptotic relations
for solutions at large distances. The power-law asymptotic relations for
-polynomials at large are governed by integer-valued matrix , where is the inverse Cartan matrix, is the
identity matrix and is permutation matrix, corresponding to a generator of
the -group of symmetry of the Dynkin diagram. The 2-form fluxes ,
, are calculated.Comment: 16 pages, Latex, no figures, prepared for a talk at RUSGRAV-16
conference in Kaliningrad, 2017, 2nd. revised version, several typos are
eliminate
Classification of Dimension 5 Lorentz Violating Interactions in the Standard Model
We give a complete classification of mass dimension five
Lorentz-non-invariant interactions composed from the Standard Model fields,
using the effective field theory approach. We identify different classes of
Lorentz violating operators, some of which are protected against transmutation
to lower dimensions even at the loop level. Within each class of operators we
determine a typical experimental sensitivity to the size of Lorentz violation.Comment: 26 page
On generalized Melvin solutions for Lie algebras of rank 3
Generalized Melvin solutions for rank- Lie algebras , and
are considered. Any solution contains metric, three Abelian 2-forms and three
scalar fields. It is governed by three moduli functions
( and is a radial variable), obeying three differential
equations with certain boundary conditions imposed. These functions are
polynomials with powers for Lie
algebras , , , respectively. The solutions depend upon
integration constants .
The power-law asymptotic relations for polynomials at large are governed
by integer-valued matrix , which coincides with twice the
inverse Cartan matrix for Lie algebras and , while in the
case , where is the identity matrix and is
a permutation matrix, corresponding to a generator of the -group
of symmetry of the Dynkin diagram. The duality identities for polynomials and
asymptotic relations for solutions at large distances are obtained. 2-form flux
integrals over a -dimensional disc of radius and corresponding Wilson
loop factors over a circle of radius are presented.Comment: 10 pages, Latex, 1 figure; 5th version: the abstract in the Latex
file is corrected. arXiv admin note: text overlap with arXiv:1706.0785
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