38 research outputs found
Refining the classification of the irreps of the 1D N-Extended Supersymmetry
The linear finite irreducible representations of the algebra of the 1D
-Extended Supersymmetric Quantum Mechanics are discussed in terms of their
"connectivity" (a symbol encoding information on the graphs associated to the
irreps). The classification of the irreducible representations with the same
fields content and different connectivity is presented up to .Comment: Two extra cases added. Reply to hep-th/0611060v2 comments adde
Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets
We furnish an algebraic understanding of the inequivalent connectivities
(computed up to ) of the graphs associated to the irreducible
supermultiplets of the N-extended Supersymmetric Quantum Mechanics. We prove
that the inequivalent connectivities of the N=5 and N=9 irreducible
supermultiplets are due to inequivalent decompositions into two sets of N=4
(respectively, N=8) supermultiplets. "Oxido-reduction" diagrams linking the
irreducible supermultiplets of the N=5,6,7,8 supersymmetries are presented. We
briefly discuss these results and their possible applications.Comment: 15 pages, 5 figure
Effects of Twisted Noncommutativity in Multi-particle Hamiltonians
The noncommutativity induced by a Drinfel'd twist produces Bopp-shift like
transformations for deformed operators. In a single-particle setting the
Drinfel'd twist allows to recover the noncommutativity obtained from various
methods which are not based on Hopf algebras. In multi-particle sector, on the
other hand, the Drinfel'd twist implies novel features. In conventional
approaches to noncommutativity, deformed primitive operators are postulated to
act additively. A Drinfel'd twist implies non-additive effects which are
controlled by the coproduct. We illustrate these features for a class of
(abelian twist-deformed) 2D Hamiltonians. Suitable choices of the parameters
lead to the Hamiltonian of the noncommutative Quantum Hall Effect, the harmonic
oscillator, the quantization of the configuration space. The non-additive
effects in the multi-particle sector, leading to results departing from the
existing literature, are pointed out.Comment: 11 page
On Light-like Deformations of the Poincar\'e Algebra
We investigate the observational consequences of the light-like deformations
of the Poincar\'e algebra induced by the jordanian and the extended jordanian
classes of Drinfel'd twists. Twist-deformed generators belonging to a Universal
Enveloping Algebra close nonlinear algebras. In some cases the nonlinear
algebra is responsible for the existence of bounded domains of the deformed
generators. The Hopf algebra coproduct implies associative nonlinear additivity
of the multi-particle states. A subalgebra of twist-deformed observables is
recovered whenever the twist-deformed generators are either hermitian or
pseudo-hermitian with respect to a common invertible hermitian operator.Comment: 18 pages; final version to appear in Eur. Phys. J.
D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics
The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the
N-extended one-dimensional Supersymmetry Algebra induce D-module
representations for the N=2,4,8 superconformal algebras.
For N=2, the D-module representations of the A(1,0) superalgebra are
obtained. For N=4 and scaling dimension \lambda=0, the D-module representations
of the A(1,1) superalgebra are obtained. For , the D-module
representations of the D(2,1;\alpha) superalgebras are obtained, with
determined in terms of the scaling dimension according to:
for k=4, i.e. the (4,4) supermultiplet,
for k=3, i.e. (3,4,1), and for k=1, i.e. (1,4,3). For
the (2,4,2) supermultiplet induces a D-module representation
for the centrally extended sl(2|2) superalgebra. For N=8, the (8,8) root
supermultiplet induces a D-module representation of the D(4,1) superalgebra at
the fixed value . A Lagrangian framework to construct
one-dimensional, off-shell, superconformal invariant actions from
single-particle and multi-particles D-module representations is discussed. It
is applied to explicitly construct invariant actions for the homogeneous and
inhomogeneous N=4 (1,4,3) D-module representations (in the last case for
several interacting supermultiplets of different chirality).Comment: 22 page
Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification
We classify the admissible types of constraint (hermitian, holomorphic, with
reality conditions on the bosonic sectors, etc.) for generalized
supersymmetries in the presence of complex spinors. We further point out which
constrained generalized supersymmetries admit a dual formulation. For both real
and complex spinors generalized supersymmetries are constructed and classified
as dimensional reductions of supersymmetries from {\em oxidized} space-times
(i.e. the maximal space-times associated to -component Clifford irreps). We
apply these results to sistematically construct a class of models describing
superparticles in presence of bosonic tensorial central charges, deriving the
consistency conditions for the existence of the action, as well as the
constrained equations of motion. Examples of these models (which, in their
twistorial formulation, describe towers of higher-spin particles) were first
introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and
Lukierski (for complex spinors).Comment: 32 pages, LaTe
Classification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics
We present an algorithmic classification of the irreps of the -extended
one-dimensional supersymmetry algebra linearly realized on a finite number of
fields. Our work is based on the 1-to-1 \cite{pt} correspondence between
Weyl-type Clifford algebras (whose irreps are fully classified) and classes of
irreps of the -extended 1D supersymmetry. The complete classification of
irreps is presented up to . The fields of an irrep are accommodated
in different spin states. N=10 is the minimal value admitting length
irreps. The classification of length-4 irreps of the N=12 and {\em real} N=11
extended supersymmetries is also explicitly presented.\par Tensoring irreps
allows us to systematically construct manifestly (-extended) supersymmetric
multi-linear invariants {\em without} introducing a superspace formalism.
Multi-linear invariants can be constructed both for {\em unconstrained} and
{\em multi-linearly constrained} fields. A whole class of off-shell invariant
actions are produced in association with each irreducible representation. The
explicit example of the N=8 off-shell action of the multiplet is
presented.\par Tensoring zero-energy irreps leads us to the notion of the {\em
fusion algebra} of the 1D -extended supersymmetric vacua.Comment: Final version to appear in JHEP. 52 pages. The part with the complete
classification of irreps (and the explicit presentation of length-4 irreps of
N=9,10,11,12 and N=10 length-5 irreps) is unchanged. An extra section has
been added with an entire class of off-shell invariant actions for arbitrary
values N of the 1D extended supersymmetry. A non-trivial N=8 off-shell action
for the (1,8,7) multiplet has been constructed as an example. It is obtained
in terms of the octonionic structure constant