4 research outputs found
Superspace formulations of the (super)twistor string
The superspace formulation of the worldvolume action of twistor string models
is considered. It is shown that for the Berkovits-Siegel closed twistor string
such a formulation is provided by a N=4 twistor-like action of the tensionless
superstring. A similar inverse twistor transform of the open twistor string
model (Berkovits model) results in a dynamical system containing two copies of
the D=4, N=4 superspace coordinate functions, one left-moving and one
right-moving, that are glued by the boundary conditions.
We also discuss possible candidates for a tensionful superstring action
leading to the twistor string in the tensionless limit as well as
multidimensional counterparts of twistor strings in the framework of both
`standard' superspace and superspace enlarged by tensorial coordinates
(tensorial superspaces), which constitute a natural framework for massless
higher spin theories.Comment: Rev Tex, 13 pages, no figure
Supersymmetric string model with 30 kappa--symmetries in an extended D=11 superspace and 30/ 32 BPS states
A supersymmetric string model in the D=11 superspace maximally extended by
antisymmetric tensor bosonic coordinates, , is proposed. It
possesses 30 -symmetries and 32 target space supersymmetries. The usual
preserved supersymmetry--symmetry correspondence suggests that it
describes the excitations of a BPS state preserving all but two
supersymmetries. The model can also be formulated in any superspace, n=32 corresponding to D=11. It may also be treated as a
`higher--spin generalization' of the usual Green--Schwarz superstring. Although
the global symmetry of the model is a generalization of the super--Poincar\'e
group, , it may be
formulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. We
work out this supertwistor realization and its Hamiltonian dynamics.
We also give the supersymmetric p-brane generalization of the model. In
particular, the supersymmetric membrane model describes
excitations of a 30/32 BPS state, as the supersymmetric
string does, while the supersymmetric 3-brane and 5-brane correspond,
respectively, to 28/32 and 24/32 BPS states.Comment: 23 pages, RevTex4. V2: minor corrections in title and terminology,
some references and comments adde
Lateral continuity and orthogonally additive operators
We generalize the notion of a laterally convergent net from increasing nets to general ones and study the corresponding lateral continuity of maps. The main result asserts that, the lateral continuity of an orthogonally additive operator is equivalent to its continuity at zero. This theorem holds for operators that send laterally convergent nets to any type convergent nets (laterally, order or norm convergent)
Points of narrowness and uniformly narrow operators
It is known that the sum of every two narrow operators on is narrow, however the same is false for with there exists a decomposition to disjoint elements such that and . The standard tool in the literature to prove the narrowness of the sum of two narrow operators is to show that the pair is uniformly narrow. We study the question of whether every pair of narrow operators with narrow sum is uniformly narrow. Having no counterexample, we prove several theorems showing that the answer is affirmative for some partial cases