160 research outputs found
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
Hidden Symmetries of the Principal Chiral Model Unveiled
By relating the two-dimensional U(N) Principal Chiral Model to a simple
linear system we obtain a free-field parametrisation of solutions. Obvious
symmetry transformations on the free-field data give symmetries of the model.
In this way all known `hidden symmetries' and B\"acklund transformations, as
well as a host of new symmetries, arise.Comment: 21 pages, Latex. A sentence and citation adde
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
Hyperkähler cones and instantons on quaternionic Kähler manifolds
We present a novel approach to the study of Yang-Mills instantons on quaternionic Kähler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperk\"ahler manifolds. Our results establish a bijection between local equivalence classes of instantons on quaternionic Kähler manifolds M and equivalence classes of certain holomorphic maps on an appropriate SL_2(C)-bundle over the Swann bundle of M
Special complex manifolds
We introduce the notion of a special complex manifold: a complex manifold
(M,J) with a flat torsionfree connection \nabla such that (\nabla J) is
symmetric. A special symplectic manifold is then defined as a special complex
manifold together with a \nabla-parallel symplectic form \omega . This
generalises Freed's definition of (affine) special K\"ahler manifolds. We also
define projective versions of all these geometries. Our main result is an
extrinsic realisation of all simply connected (affine or projective) special
complex, symplectic and K\"ahler manifolds. We prove that the above three types
of special geometry are completely solvable, in the sense that they are locally
defined by free holomorphic data. In fact, any special complex manifold is
locally realised as the image of a holomorphic 1-form \alpha : C^n \to T^* C^n.
Such a realisation induces a canonical \nabla-parallel symplectic structure on
M and any special symplectic manifold is locally obtained this way. Special
K\"ahler manifolds are realised as complex Lagrangian submanifolds and
correspond to closed forms \alpha. Finally, we discuss the natural geometric
structures on the cotangent bundle of a special symplectic manifold, which
generalise the hyper-K\"ahler structure on the cotangent bundle of a special
K\"ahler manifold.Comment: 24 pages, latex, section 3 revised (v2), modified Abstract and
Introduction, version to appear in J. Geom. Phy
Killing spinors are Killing vector fields in Riemannian Supergeometry
A supermanifold M is canonically associated to any pseudo Riemannian spin
manifold (M_0,g_0). Extending the metric g_0 to a field g of bilinear forms
g(p) on T_p M, p\in M_0, the pseudo Riemannian supergeometry of (M,g) is
formulated as G-structure on M, where G is a supergroup with even part G_0\cong
Spin(k,l); (k,l) the signature of (M_0,g_0). Killing vector fields on (M,g)
are, by definition, infinitesimal automorphisms of this G-structure. For every
spinor field s there exists a corresponding odd vector field X_s on M. Our main
result is that X_s is a Killing vector field on (M,g) if and only if s is a
twistor spinor. In particular, any Killing spinor s defines a Killing vector
field X_s.Comment: 14 pages, latex, one typo correcte
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