124 research outputs found
Division Algebras and Extended SuperKdVs
The division algebras R, C, H, O are used to construct and analyze the
N=1,2,4,8 supersymmetric extensions of the KdV hamiltonian equation. In
particular a global N=8 super-KdV system is introduced and shown to admit a
Poisson bracket structure given by the "Non-Associative N=8 Superconformal
Algebra".Comment: 6 pages, LaTex; Talk given at the XXXVII Karpacz Winter School in
Theoretical Physics (February 2001). To appear in the proceeding
On non-minimal N=4 supermultiplets in 1D and their associated sigma-models
We construct the non-minimal linear representations of the N=4 Extended
Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields.
Inequivalent representations are specified by the mass-dimension of the fields
and the connectivity of the associated graphs. The oxidation to minimal N=5
linear representations is given. Two types of N=4 sigma-models based on
non-minimal representations are obtained: the resulting off-shell actions are
either manifestly invariant or depend on a constrained prepotential. The
connectivity properties of the graphs play a decisive role in discriminating
inequivalent actions. These results find application in partial breaking of
supersymmetric theories.Comment: 24 pages, 6 figure
Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the
N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means
that they admit at least one graphical presentation (the corresponding
graph/graphs are known as "Adinkras"). We further prove the existence of
"entangled" linear supermultiplets which do not admit a graphical presentation,
by constructing an explicit example of an entangled N=4 supermultiplet with
field content (3,8,5). It interpolates between two inequivalent pure N=4
supermultiplets with the same field content. The one-dimensional N=4
sigma-model with a three-dimensional target based on the entangled
supermultiplet is presented. The distinction between the notion of equivalence
for pure supermultiplets and the notion of equivalence for their associated
graphs (Adinkras) is discussed. Discrete properties such as chirality and
coloring can discriminate different supermultiplets. The tools used in our
classification include, among others, the notion of field content, connectivity
symbol, commuting group, node choice group and so on.Comment: 20 pages, 5 figures. Two references adde
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