5,582 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
On Supermultiplet Twisting and Spin-Statistics
Twisting of off-shell supermultiplets in models with 1+1-dimensional
spacetime has been discovered in 1984, and was shown to be a generic feature of
off-shell representations in worldline supersymmetry two decades later. It is
shown herein that in all supersymmetric models with spacetime of four or more
dimensions, this off-shell supermultiplet twisting, if non-trivial, necessarily
maps regular (non-ghost) supermultiplets to ghost supermultiplets. This feature
is shown to be ubiquitous in all fully off-shell supersymmetric models with
(BV/BRST-treated) constraints.Comment: Extended version, including a new section on manifestly off-shell and
supersymmetric BRST treatment of gauge symmetry; added reference
Chiral supergravity actions and superforms
The superform construction of supergravity actions, christened the "ectoplasm
method," is based on the use of a closed super d-form in the case of d
space-time dimensions. In known examples, such superforms are obtained by
iteratively solving nontrivial cohomological problems. The latter usually makes
this scheme no less laborious than the normal coordinate method for deriving
component actions for matter-coupled supergravity. In this note we present an
alternative procedure to generate required superforms in four space-time
dimensions, which makes use of self-dual vector multiplets. It provides the
shortest derivation of chiral actions in two different theories: (i) N = 1 old
minimal supergravity; and (ii) N = 2 conformal supergravity. The N = 2
superform construction is developed here for the first time. Although our
consideration is restricted to the case of four dimensions, a generalization to
higher dimensions is plausible.Comment: 14 pages; V2: minor correction
A Superfield for Every Dash-Chromotopology
The recent classification scheme of so-called adinkraic off-shell
supermultiplets of N-extended worldline supersymmetry without central charges
finds a combinatorial explosion. Completing our earlier efforts, we now
complete the constructive proof that all of these trillions or more of
supermultiplets have a superfield representation. While different as
superfields and supermultiplets, these are still super-differentially related
to a much more modest number of minimal supermultiplets, which we construct
herein.Comment: 13 pages, integrated illustration
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
Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras
We compute the short distance expansion of fields or operators that live in
the coadjoint representation of an infinite dimensional Lie algebra by using
only properties of the adjoint representation and its dual. We explicitly
compute the short distance expansion for the duals of the Virasoro algebra,
affine Lie Algebras and the geometrically realized N-extended supersymmetric GR
Virasoro algebra.Comment: 19 pages, LaTeX twice, no figure, replacement has corrected Lie
algebr
Nonequilibrium stationary states with Gibbs measure for two or three species of interacting particles
We construct explicit examples of one-dimensional driven diffusive systems
for two and three species of interacting particles, defined by asymmetric
dynamical rules which do not obey detailed balance, but whose nonequilibrium
stationary-state measure coincides with a prescribed equilibrium Gibbs measure.
For simplicity, the measures considered in this construction only involve
nearest-neighbor interactions. For two species, the dynamics thus obtained
generically has five free parameters, and does not obey pairwise balance in
general. The latter property is satisfied only by the totally asymmetric
dynamics and the partially asymmetric dynamics with uniform bias, i.e., the
cases originally considered by Katz, Lebowitz, and Spohn. For three species of
interacting particles, with nearest-neighbor interactions between particles of
the same species, the totally asymmetric dynamics thus obtained has two free
parameters, and obeys pairwise balance. These models are put in perspective
with other examples of driven diffusive systems. The emerging picture is that
asymmetric (nonequilibrium) stochastic dynamics leading to a given
stationary-state measure are far more constrained (in terms of numbers of free
parameters) than the corresponding symmetric (equilibrium) dynamics.Comment: 18 pages, 8 tables, 1 figure. Stylistic and other minor improvement
A Derivation of an Off-Shell N = (2,2) Supergravity Chiral Projection Operator
Utilizing the known off-shell formulation of 2D, N = (2,2) supergravity,
containing a finite number of auxiliary fields, there is shown to exist a
simple form for a 'chiral projection operator' and an explicit expression for
it is given.Comment: 10 pages, no figures, one new reference adde
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