1,611 research outputs found
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
The Real Anatomy of Complex Linear Superfields
Recent work on classicication of off-shell representations of N-extended
worldline supersymmetry without central charges has uncovered an unexpectedly
vast number--trillions of even just (chromo)topology types--of so called
adinkraic supermultiplets. Herein, we show by explicit analysis that a
long-known but rarely used representation, the complex linear supermultiplet,
is not adinkraic, cannot be decomposed locally, but may be reduced by means of
a Wess-Zumino type gauge. This then indicates that the already unexpectedly
vast number of adinkraic off-shell supersymmetry representations is but the
proverbial tip of the iceberg.Comment: 21 pages, 4 figure
Variant Supercurrents and Linearized Supergravity
In this paper the variant supercurrents based on consistency and completion
in off-shell N=1 supergravity are studied. We formulate the embedding relations
for supersymmetric current and energy tensor into supercurrent multiplet.
Corresponding linearized supergravity is obtained with appropriate choice of
Wess-Zumino gauge in each gravity supermultiplet.Comment: v1: 9 pp; v2: minor changes; v3: 10 pp, published versio
Variant supercurrents and Noether procedure
Consistent supercurrent multiplets are naturally associated with linearized
off-shell supergravity models. In arXiv:1002.4932 we presented the hierarchy of
such supercurrents which correspond to all the models for linearized 4D N = 1
supergravity classified a few years ago. Here we analyze the correspondence
between the most general supercurrent given in arXiv:1002.4932 and the one
obtained eight years ago in hep-th/0110131 using the superfield Noether
procedure. We apply the Noether procedure to the general N = 1 supersymmetric
nonlinear sigma-model and show that it naturally leads to the so-called
S-multiplet, revitalized in arXiv:1002.2228.Comment: 6 page
On the Construction and the Structure of Off-Shell Supermultiplet Quotients
Recent efforts to classify representations of supersymmetry with no central
charge have focused on supermultiplets that are aptly depicted by Adinkras,
wherein every supersymmetry generator transforms each component field into
precisely one other component field or its derivative. Herein, we study
gauge-quotients of direct sums of Adinkras by a supersymmetric image of another
Adinkra and thus solve a puzzle from Ref.[2]: The so-defined supermultiplets do
not produce Adinkras but more general types of supermultiplets, each depicted
as a connected network of Adinkras. Iterating this gauge-quotient construction
then yields an indefinite sequence of ever larger supermultiplets, reminiscent
of Weyl's construction that is known to produce all finite-dimensional unitary
representations in Lie algebras.Comment: 20 pages, revised to clarify the problem addressed and solve
Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration
We discuss four off-shell N=4 D=1 supersymmetry transformations, their
associated one-dimensional sigma-models and their mutual relations. They are
given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of
R^4), II) the (3,4,1)_{lin} linear supermultiplet (supersymmetric extension of
R^3), III) the (3,4,1)_{nl} non-linear supermultiplet living on S^3 and IV) the
(2,4,2)_{nl} non-linear supermultiplet living on S^2. The I -> II map is the
supersymmetric extension of the R^4 -> R^3 bilinear map, while the II -> IV map
is the supersymmetric extension of the S^3 -> S^2 first Hopf fibration. The
restrictions on the S^3, S^2 spheres are expressed in terms of the
stereographic projections. The non-linear supermultiplets, whose
supertransformations are local differential polynomials, are not equivalent to
the linear supermultiplets with the same field content. The sigma-models are
determined in terms of an unconstrained prepotential of the target coordinates.
The Uniformization Problem requires solving an inverse problem for the
prepotential. The basic features of the supersymmetric extension of the second
and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the
real, complex or quaternionic property) is extended to all minimal linear
supermultiplets up to N<=8.Comment: 24 page
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
Variant supercurrent multiplets
In N = 1 rigid supersymmetric theories, there exist three standard
realizations of the supercurrent multiplet corresponding to the (i) old
minimal, (ii) new minimal and (iii) non-minimal off-shell formulations for N =
1 supergravity. Recently, Komargodski and Seiberg in arXiv:1002.2228 put
forward a new supercurrent and proved its consistency, although in the past it
was believed not to exist. In this paper, three new variant supercurrent
multiplets are proposed. Implications for supergravity-matter systems are
discussed.Comment: 11 pages; V2: minor changes in sect. 3; V3: published version; V4:
typos in eq. (2.3) corrected; V5: comments and references adde
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