644 research outputs found
A BPS Interpretation of Shape Invariance
We show that shape invariance appears when a quantum mechanical model is
invariant under a centrally extended superalgebra endowed with an additional
symmetry generator, which we dub the shift operator. The familiar mathematical
and physical results of shape invariance then arise from the BPS structure
associated with this shift operator. The shift operator also ensures that there
is a one-to-one correspondence between the energy levels of such a model and
the energies of the BPS-saturating states. These findings thus provide a more
comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe
Adinkras: A Graphical Technology for Supersymmetric Representation Theory
We present a symbolic method for organizing the representation theory of
one-dimensional superalgebras. This relies on special objects, which we have
called adinkra symbols, which supply tangible geometric forms to the
still-emerging mathematical basis underlying supersymmetry.Comment: 44 pages, LaTeX, 35 figure
Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry
A minimal representation of the N = 8 extended worldline supersymmetry, known
as the `ultra-multiplet', is closely related to a family of supermultiplets
with the same, E(8) chromotopology. We catalogue their effective symmetries and
find a Spin(4) x Z(2) subgroup common to them all, which explains the
particular basis used in the original construction. We specify a constrained
superfield representation of the supermultiplets in the ultra-multiplet family,
and show that such a superfield representation in fact exists for all adinkraic
supermultiplets. We also exhibit the correspondences between these
supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we
construct quadratic Lagrangians that provide the standard kinetic terms and
afford a mixing of an even number of such supermultiplets controlled by a
coupling to an external 2-form of fluxes.Comment: 13 Figure
On the Duality between Perturbative Heterotic Orbifolds and M-Theory on T^4/Z_N
The heterotic string compactified on an orbifold T^4/\IZ_N
has gauge group with (massless) states in its twisted sectors
which are charged under both gauge group factors. In the dual M-theory on
(T^4/\IZ_N)\otimes(S^1/\IZ_2) the two group factors are separated in the
eleventh direction and the G and G' gauge fields are confined to the two
boundary planes, respectively. We present a scenario which allows for a
resolution of this apparent paradox and assigns all massless matter multiplets
locally to the different six-dimensional boundary fixed planes. The resolution
consists of diagonal mixing between the gauge groups which live on the
connecting seven-planes (6d and the eleventh dimension) and one of the gauge
group factors. We present evidence supporting this mixing by considering gauge
couplings and verify local anomaly cancellation. We also discuss open problems
which arise in the presence of U_1 factors.Comment: 45 pages, one figur
Codes and Supersymmetry in One Dimension
Adinkras are diagrams that describe many useful supermultiplets in D=1
dimensions. We show that the topology of the Adinkra is uniquely determined by
a doubly even code. Conversely, every doubly even code produces a possible
topology of an Adinkra. A computation of doubly even codes results in an
enumeration of these Adinkra topologies up to N=28, and for minimal
supermultiplets, up to N=32.Comment: 48 pages, a new version that combines arXiv:0811.3410 and parts of
arXiv:0806.0050, for submission for publicatio
On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields
In this paper we discuss off-shell representations of N-extended
supersymmetry in one dimension, ie, N-extended supersymmetric quantum
mechanics, and following earlier work on the subject codify them in terms of
certain graphs, called Adinkras. This framework provides a method of generating
all Adinkras with the same topology, and so also all the corresponding
irreducible supersymmetric multiplets. We develop some graph theoretic
techniques to understand these diagrams in terms of a relatively small amount
of information, namely, at what heights various vertices of the graph should be
"hung".
We then show how Adinkras that are the graphs of N-dimensional cubes can be
obtained as the Adinkra for superfields satisfying constraints that involve
superderivatives. This dramatically widens the range of supermultiplets that
can be described using the superspace formalism and organizes them. Other
topologies for Adinkras are possible, and we show that it is reasonable that
these are also the result of constraining superfields using superderivatives.
The family of Adinkras with an N-cubical topology, and so also the sequence
of corresponding irreducible supersymmetric multiplets, are arranged in a
cyclical sequence called the main sequence. We produce the N=1 and N=2 main
sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte
4D, N = 1 Supersymmetry Genomics (II)
We continue the development of a theory of off-shell supersymmetric
representations analogous to that of compact Lie algebras such as SU(3). For
off-shell 4D, N = 1 systems, quark-like representations have been identified
[1] in terms of cis-Adinkras and trans-Adinkras and it has been conjectured
that arbitrary representations are composites of -cis and -trans
representations. Analyzing the real scalar and complex linear superfield
multiplets, these "chemical enantiomer" numbers are found to be = =
1 and = 1, = 2, respectively.Comment: 40 pages, 8 figures, sequel to "4D, N = 1 Supersymmetry Genomics (I)"
[arxiv: 0902.3830
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