504 research outputs found
On algebraic supergroups, coadjoint orbits and their deformations
In this paper we study algebraic supergroups and their coadjoint orbits as
affine algebraic supervarieties. We find an algebraic deformation quantization
of them that can be related to the fuzzy spaces of non commutative geometry.Comment: 37 pages, AMS-LaTe
A Comparison between Star Products on Regular Orbits of Compact Lie Groups
In this paper an algebraic star product and differential one defined on a
regular coadjoint orbit of a compact semisimple group are compared. It is
proven that there is an injective algebra homomorphism between the algebra of
polynomials with the algebraic star product and the algebra of differential
functions with the differential star product structure.Comment: AMS-LaTeX, 19 pages. Version to appear in the Journal of Physics
On the Embedding of Space-Time Symmetries into Simple Superalgebras
We explore the embedding of Spin groups of arbitrary dimension and signature
into simple superalgebras in the case of extended supersymmetry. The
R-symmetry, which generically is not compact, can be chosen compact for all the
cases that are congruent mod 8 to the physical conformal algebra so(,2),
. An grading of the superalgebra is found in all cases.
Central extensions of super translation algebras are studied in this framework.Comment: AMS LaTeX, 16 page
The quantum chiral Minkowski and conformal superspaces
We give a quantum deformation of the chiral super Minkowski space in four
dimensions as the big cell inside a quantum super Grassmannian. The
quantization is performed in such way that the actions of the Poincar\'e and
conformal quantum supergroups on the quantum Minkowski and quantum conformal
superspaces are presented.Comment: 54 page
On the deformation quantization of affine algebraic varieties
We compute an explicit algebraic deformation quantization for an affine
Poisson variety described by an ideal in a polynomial ring, and inheriting its
Poisson structure from the ambient space.Comment: AMS-LaTeX, 20 page
On the Super Higgs Effect in Extended Supergravity
We consider the reduction of supersymmetry in N-extended four dimensional
supergravity via the super Higgs mechanism in theories without cosmological
constant. We provide an analysis largely based on the properties of long and
short multiplets of Poincare' supersymmetry. Examples of the super Higgs
phenomenon are realized in spontaneously broken N=8 supergravity through the
Scherk-Schwarz mechanism and in superstring compactification in presence of
brane fluxes. In many models the massive vectors count the difference in number
of the translation isometries of the scalar sigma-model geometries in the
broken and unbroken phase.Comment: Version to appear on Nuclear Physics
Quadratic deformation of Minkowski space
We present a deformation of the Minkowski space as embedded into the
conformal space (in the formalism of twistors) based in the quantum versions of
the corresponding kinematic groups. We compute explicitly the star product,
whose Poisson bracket is quadratic. We show that the star product although
defined on the polynomials can be extended differentiably. Finally we compute
the Eucliden and Minkowskian real forms of the deformation.Comment: Presented at XVII European Workshop on String Theory 2011. Padova
(Italy) September 05-09; Fortschr. Phys. 1-7 (2012
quantum chiral superfields and quantum super bundles
We give the superalgebra of chiral (and antichiral) quantum superfields
realized as a subalgebra of the quantum supergroup . The
multiplication law in the quantum supergroup induces a coaction on the set of
chiral superfields. We also realize the quantum deformation of the chiral
Minkowski superspace as a quantum principal bundle
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