617 research outputs found
Lorentz covariant spin two superspaces
Superalgebras including generators having spins up to two and realisable as
tangent vector fields on Lorentz covariant generalised superspaces are
considered. The latter have a representation content reminiscent of
configuration spaces of (super)gravity theories. The most general canonical
supercommutation relations for the corresponding phase space coordinates
allowed by Lorentz covariance are discussed. By including generators
transforming according to every Lorentz representation having spin up to two,
we obtain, from the super Jacobi identities, the complete set of quadratic
equations for the Lorentz covariant structure constants. These defining
equations for spin two Heisenberg superalgebras are highly overdetermined.
Nevertheless, non-trivial solutions can indeed be found. By making some
simplifying assumptions, we explicitly construct several classes of these
superalgebras.Comment: 20 pages, latex, typos correcte
Democratic Supersymmetry
We present generalisations of N-extended supersymmetry algebras in four
dimensions, using Lorentz covariance and invariance under permutation of the N
supercharges as selection criteria.Comment: 26 pages, latex fil
Self-duality in Generalized Lorentz Superspaces
We extend the notion of self-duality to spaces built from a set of
representations of the Lorentz group with bosonic or fermionic behaviour, not
having the traditional spin-one upper-bound of super Minkowski space. The
generalized derivative vector fields on such superspaces are assumed to form a
superalgebra. Introducing corresponding gauge potentials and hence covariant
derivatives and curvatures, we define generalized self-duality as the Lorentz
covariant vanishing of certain irreducible parts of the curvatures.Comment: 6 pages, Late
Extended Self-Dual Yang-Mills from the N=2 String
We show that the physical degrees of freedom of the critical open string with
N=2 superconformal symmetry on the worldsheet are described by a self-dual
Yang-Mills field on a hyperspace parametrised by the coordinates of the target
space R^{2,2} together with a commuting chiral spinor. A prepotential for the
self-dual connection in the hyperspace generates the infinite tower of physical
fields corresponding to the inequivalent pictures or spinor ghost vacua of this
string. An action is presented for this tower, which describes consistent
interactions amongst fields of arbitrarily high spin. An interesting truncation
to a theory of five fields is seen to have no graphs of two or more loops.Comment: 19 pages; typos corrected, note and reference added; published
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Unravelling the On-shell Constraints of Self-dual Supergravity Theories
We review a construction, using the harmonic space method, of solutions to
the superfield equations of motion for N-extended self-dual supergravity
theories. A superspace gauge condition suitable for the performance of a
component analysis is discussed.Comment: 5 pages, latex using espcrc2.sty, talk at the 29th International
Ahreshoop Symposium, Buckow, August 199
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
String-induced Yang-Mills coupling to self-dual gravity
By considering N=2 string amplitudes we determine the (2+2)-dimensional
target space action for the physical degrees of freedom: self-dual gravity and
self-dual Yang-Mills, together with their respective infinite towers of
higher-spin inequivalent picture states. Novel `stringy' couplings amongst
these fields are essential ingredients of an action principle for the effective
target space field theory. We discuss the covariant description of this theory
in terms of self-dual fields on a hyperspace parametrised by the target space
coordinate and a commuting chiral spinor.Comment: 20 pages, no figure
Super self-duality for Yang-Mills fields in dimensions greater than four
Self-duality equations for Yang-Mills fields in d-dimensional Euclidean
spaces consist of linear algebraic relations amongst the components of the
curvature tensor which imply the Yang-Mills equations. For the extension to
superspace gauge fields, the super self-duality equations are investigated,
namely, systems of linear algebraic relations on the components of the
supercurvature, which imply the self-duality equations on the even part of
superspace. A group theory based algorithm for finding such systems is
developed. Representative examples in various dimensions are provided,
including the Spin(7) and G(2) invariant systems in d=8 and 7, respectively.Comment: 51 pages, late
Conserved currents for unconventional supersymmetric couplings of self-dual gauge fields
Self-dual gauge potentials admit supersymmetric couplings to higher-spin
fields satisfying interacting forms of the first order Dirac--Fierz equation.
The interactions are governed by conserved currents determined by
supersymmetry. These super-self-dual Yang-Mills systems provide on-shell
supermultiplets of arbitrarily extended super-Poincar\'e algebras; classical
consistency not setting any limit on the extension N. We explicitly display
equations of motion up to the extension. The stress tensor, which
vanishes for the self-duality equations, not only gets resurrected
when , but is then a member of a conserved multiplet of gauge-invariant
tensors.Comment: 6 pages, latex fil
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