2,753 research outputs found
Superbranes, D=11 CJS supergravity and enlarged superspace coordinates/fields correspondence
We discuss the r\^ole of enlarged superspaces in two seemingly different
contexts, the structure of the -brane actions and that of the
Cremmer-Julia-Scherk eleven-dimensional supergravity. Both provide examples of
a common principle: the existence of an {\it enlarged superspaces
coordinates/fields correspondence} by which all the (worldvolume or spacetime)
fields of the theory are associated to coordinates of enlarged superspaces. In
the context of -branes, enlarged superspaces may be used to construct
manifestly supersymmetry-invariant Wess-Zumino terms and as a way of expressing
the Born-Infeld worldvolume fields of D-branes and the worldvolume M5-brane
two-form in terms of fields associated to the coordinates of these enlarged
superspaces. This is tantamount to saying that the Born-Infeld fields have a
superspace origin, as do the other worldvolume fields, and that they have a
composite structure. In =11 supergravity theory enlarged superspaces arise
when its underlying gauge structure is investigated and, as a result, the
composite nature of the field is revealed: there is a full one-parametric
family of enlarged superspace groups that solve the problem of expressing
in terms of spacetime fields associated to their coordinates. The corresponding
enlarged supersymmetry algebras turn out to be deformations of an {\it
expansion} of the algebra. The unifying mathematical structure
underlying all these facts is the cohomology of the supersymmetry algebras
involved.Comment: plain latex, 29 pages, no figures. To appear in the Am. Inst. of
Phys. Proc. Serie
Quaternionic (super)twistors extensions and general superspaces
In a attempt to treat a supergravity as a tensor representation, the
4-dimensional N-extended quaternionic superspaces are constructed from the
(diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation,
performed in a previous work of the authors[14], with N = p + k: These
quaternionic superspaces have 4 + k (N - k) even-quaternionic coordinates and
4N odd- quaternionic coordinates where each coordinate is a quaternion composed
by four C-felds (bosons and fermions respectively). The fields content as the
dimensionality (even and odd sectors) of these superspaces are given and
exemplified by selected physical cases. In this case the number of felds of the
supergravity is determined by the number of components of the tensor
representation of the 4-dimensional N-extended quaternionic superspaces. The
role of tensorial central charges for any N even USp (N) = Sp (N;HC) \ U (N;HC)
is elucidated from this theoretical context.Comment: To be published in the IJGMMP 2016, corrected version, 16 pages
without figure
Generalised supersymmetry and p-brane actions
We investigate the most general N=1 graded extension of the Poincare algebra,
and find the corresponding supersymmetry transformations and the associated
superspaces. We find that the supersymmetry for which {Q,Q} = P is not special,
and in fact must be treated democratically with a whole class of
supersymmetries. We show that there are two distinct types of grading, and a
new class of general spinors is defined. The associated superspaces are shown
to be either of the usual type, or flat with no torsion. p-branes are discussed
in these general superspaces and twelve dimensions emerges as maximal. New
types of brane are discovered which could explain many features of the standard
p-brane theories.Comment: 29 pages, LaTex, no figures. Errors in degrees of freedom counting
corrected, leading to altered brane sca
Supersymmetric Lorentz-Covariant Hyperspaces and self-duality equations in dimensions greater than (4|4)
We generalise the notions of supersymmetry and superspace by allowing
generators and coordinates transforming according to more general Lorentz
representations than the spinorial and vectorial ones of standard lore. This
yields novel SO(3,1)-covariant superspaces, which we call hyperspaces, having
dimensionality greater than (4|4) of traditional super-Minkowski space. As an
application, we consider gauge fields on complexifications of these
superspaces; and extending the concept of self-duality, we obtain classes of
completely solvable equations analogous to the four-dimensional self-duality
equations.Comment: 29 pages, late
The symplectic origin of conformal and Minkowski superspaces
Supermanifolds provide a very natural ground to understand and handle
supersymmetry from a geometric point of view; supersymmetry in and
dimensions is also deeply related to the normed division algebras.
In this paper we want to show the link between the conformal group and
certain types of symplectic transformations over division algebras. Inspired by
this observation we then propose a new\,realization of the real form of the 4
dimensional conformal and Minkowski superspaces we obtain, respectively, as a
Lagrangian supermanifold over the twistor superspace and a
big cell inside it.
The beauty of this approach is that it naturally generalizes to the 6
dimensional case (and possibly also to the 10 dimensional one) thus providing
an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change
Three-dimensional (p,q) AdS superspaces and matter couplings
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions,
with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS
superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with
(p,q) AdS supersymmetry exist for p+q4 the target space geometries
are highly restricted). Here we concentrate on studying off-shell N=3
supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we
give three different realisations of the supersymmetric action. We show that
(3,0) AdS supersymmetry requires the sigma-model to be superconformal, and
hence the corresponding target space is a hyperkahler cone. In the case of
(2,1) AdS supersymmetry, the sigma-model target space must be a non-compact
hyperkahler manifold endowed with a Killing vector field which generates an
SO(2) group of rotations of the two-sphere of complex structures.Comment: 52 pages; V3: minor corrections, version published in JHE
Superanalogs of the Calogero operators and Jack polynomials
A depending on a complex parameter superanalog
of Calogero operator is constructed; it is related with the root system of the
Lie superalgebra . For we obtain the usual Calogero
operator; for we obtain, up to a change of indeterminates and parameter
the operator constructed by Veselov, Chalykh and Feigin [2,3]. For the operator is the radial part of the 2nd
order Laplace operator for the symmetric superspaces corresponding to pairs
and , respectively. We will show
that for the generic and the superanalogs of the Jack polynomials
constructed by Kerov, Okunkov and Olshanskii [5] are eigenfunctions of
; for they coinside with the spherical
functions corresponding to the above mentioned symmetric superspaces. We also
study the inner product induced by Berezin's integral on these superspaces
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