Central Charge Coordinates Research Articles

BPS preons and tensionless super-p-branes in generalized superspace

Tensionless super-p-branes in a generalized superspace with additional tensorial central charge coordinates may provide an extended object model for BPS preons, i.e., for the hypothetical constituents of M-theory preserving 31 of 32 supersymmetries [I.A. Bandos, J.A. de Azcárraga, J.M. Izquierdo, J. Lukierski, Phys. Rev. Lett. 86 (2001) 4451].

Exactly solvable p-brane model with extra supersymmetry

Effect of the supersymmetry enhancement due to the presence of tensor central charge coordinates in the models of tensionless superstring and superbrane is studied. Exactly solvable super p-brane model preserving 3/4 of the D=4, N=1 supersymmetry is presented. The fine tuning of extra κ-symmetry with the R-symmetry is observed. We show that the general solution for the Goldstone fermion is pure static.

Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates

A new class of twistor-like string models in four-dimensional space-time extended by the addition of six tensorial central charge (TCC) coordinates $z_{mn}$ is studied. The Hamiltonian of tensionless string in the extended space-time is derived and its symmetries are investigated. We establish that the string constraints reduce the number of independent TCC coordinates $z_{mn}$ to one real effective coordinate which composes an effective 5-dimensional target space together with the $x^{m}$ coordinates. We construct the P.B. algebra of the first class constraints and discover that it coincides with the P.B. algebra of tensionless strings. The Lorentz covariant antisymmetric Dirac $\hat{\mathbf C}$-matrix of the P.B. of the second class constraints is constructed and its algebraic structure is further presented.

Uniform twistor-like formulation of massive and massless superparticles with tensorial central charges

We construct the manifestly Lorentz-invariant twistorial formulation of the N = 1 D = 4 superparticle with tensorial central charges which describes massive and massless cases in a uniform manner. The tensorial central charges are realized in terms of even spinor variables and central charge coordinates. The full analysis of the number of conserved supersymmetries has been carried out. In the massive case the superparticle preserves 1 4 or 1 2 of target-space supersymmetries whereas the massless superparticle preserves two or three supersymmetries.

Strings in space with tensor central charge coordinates

New string models in D = 4 space-time extended by tensor central charge coordinates z mn are constructed. We use the z mn coordinates to generate string tension using a minimally extended string action linear in dz mn . It is shown that the presence of z mn lifts the light-like character of the tensionless string worldsheet and the degeneracy of its induced metric. We analyse the equations of motion and find a solution of the string equations in the generalized D=(4+6)-dimensional space X M = ( x m , z mn ) with z mn describing a spin wave process. A supersymmetric version of the proposed model is formulated.

Superparticle models with tensorial central charges

A generalization of the Ferber-Shirafuji formulation of superparticle mechanics is considered. The generalized model describes the dynamics of a superparticle in a superspace extended by tensorial central charge coordinates and commuting twistorlike spinor variables. The $D=4$ model contains a continuous real parameter $a>~0$ and at $a=0$ reduces to the $SU(2,2|1)$ supertwistor Ferber-Shirafuji model, while at $a=1$ one gets an $OSp(1|8)$ supertwistor model proposed by two of the authors which describes BPS states with all but one unbroken target space supersymmetries. When $0<a<1$ the model admits an $OSp(2|8)$ supertwistor description, and when $a>1$ the supertwistor group becomes $OSp(1,1|8).$ We quantize the model and find that its quantum spectrum consists of massless states of an arbitrary (half-)integer helicity. The independent discrete central charge coordinate describes the helicity spectrum. We also outline the generalization of the $a=1$ model to higher space-time dimensions and demonstrate that in $D=3,$ 4, 6, and 10, where the quantum states are massless, the extra degrees of freedom (with respect to that of the standard superparticle) parametrize compact manifolds. These compact manifolds can be associated with higher-dimensional helicity states. In particular, in $D=10$ the additional ``helicity'' manifold is isomorphic to the sphere ${S}^{7}.$

Gauge field geometry from complex and harmonic analyticities II. Hyper-Kähler case

The concept of preservation of harmonic analyticity is applied to find unconstrained prepotentials of hyper-Kähler geometry. We rewrite the R 4 n ( n = 1, 2, …) hyper-Kähler constraints in the harmonic space R 4 n × S 2 and then solve them in terms of two prepotentials defined in an analytic subspace. The geometric meaning of prepotentials is revealed with introducing extra central charge coordinates. Working in the analytic basis permits one to define the metric by solving a linear differential equation on S 2. The procedure is illustrated by the Taub-NUT example. We also reproduce the well-known Ward ansatz for the metric and discuss the relation to twistor approaches. Finally, we establish the one-to-one correspondence between hyper-Kähler geometry and off-shell d = 4, N = 2 supersymmetric σ models. Their most general Lagrangian is shown to be uniquely composed of hyper-Kähler prepotentials, with the analytic space coordinates replaced by analytic hypermultiplet superfields defined on the same set of harmonic variables.