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.Comment: 18 pages, Latex, no figure

Wess-Zumino actions and Dirichlet Boundary Conditions for Super p-branes with Exotic Fractions of Supersymmetry

The general solutions in the models of closed and open superstring and super p-branes with exotic fractions of the N=1 supersymmetry are considered and the spontaneously broken character of the $OSp(1,2M)$ symmetry of the models is established. It is shown that extending these models by Wess-Zumino terms generates the Dirichlet boundary conditions for superstring and super p-branes. Using the generalized Wess-Zumino terms new $OSp(1,2M)$ invariant super p-brane and Dp-brane-like actions preserving $\frac{M-1}{M}$ fraction of supersymmetry are proposed. For M=32 these models suggest new superbrane vacua of M-theory preserving 31 from 32 global supersymmetries.Comment: Latex, 13 page

Variational principle and a perturbative solution of non-linear string equations in curved space

String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension $\epsilon=\gamma/\alpha^{\prime}$, where $\gamma$ is a metric parametrizing constant. A rescaled slow worldsheet time $T=\epsilon\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\epsilon$-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H (\alpha^{\prime}H^{2}\gg1)$.Comment: 22 pages, LATEX, no figure

Type IIB tensionless superstrings in a pp-wave background

We solve the tensionless string in a constant plane wave background and obtain a hugely degenerate spectrum. This is the case for a large class of plane wave backgrounds. We show that the solution can also be derived as a consistent limit of the quantized tensile theory of IIB strings in a pp-wave. This is in contrast to the situation for several other backgrounds.Comment: 1+17 pages, LaTeX, minor corrections, added new reference

Toroidal p-branes, anharmonic oscillators and (hyper)elliptic solutions

Exact solvability of brane equations is studied, and a new $U(1)\times U(1)\times... \times U(1)$ invariant anzats for the solution of $p$-brane equations in $D=(2p+1)$-dimensional Minkowski space is proposed. The reduction of the $p$-brane Hamiltonian to the Hamiltonian of $p$-dimensional relativistic anharmonic oscillator with the monomial potential of the degree equal to $2p$ is revealed. For the case of degenerate p-torus with equal radii it is shown that the $p$-brane equations are integrable and their solutions are expressed in terms of elliptic ($p=2$) or hyperelliptic ($p>2$) functions. The solution describes contracting $p$-brane with the contraction time depending on $p$ and the brane energy density. The toroidal brane elasticity is found to break down linear Hooke law as it takes place for the anharmonic elasticity of smectic liquid crystals.Comment: 18 pages, extended version accepted in Nucl. Phys. B; discussions on integrability and geometric approach added; correspondence between anharmonic elasticity in toroidal branes and smectic liquid crystals revealed; references and acknowledgements updated; typos correcte

Extra Gauge Symmetry for Extra Supersymmetry

It is shown that the extra supersymmetry of tensionless superstring and super $p$-brane is accompanied by the presence of new bosonic gauge symmetries. It permits to use composed coordinates encoding all physical degrees of freedom of the model and invariant under these gauge symmetries and the enhanced $\kappa$-symmetry. It is proved that the composed gauge invariant coordinates coincide with the componets of symplectic supertwistor realizing a linear representation of the hidden OSp(1,2M) symmetry of the super $p$-brane Lagrangian. A connection of the presented gauge symmetries with massless higher spin gauge theories and a symmetric phase of $M$/string-theory is discussed.Comment: Latex, 10 pages; references and few comments added for section 1. To appear in Phys. Lett.

Generalized hooke law for relativistic membranes and p-branes

The character of elastic forces of relativistic membranes and p-branes encoded in their nonlinear equations is studied. The toroidal brane equations are reduced to the classical equations of anharmonic elastic media described by monomial potentials. Integrability of the equations is discussed and some of their exact solutions are constructed.Исследуется характер сил упругости, задаваемых нелинейными уравнениями релятивистских мембран и р-бран. Уравнения тороидальных бран преобразуются к классическим уравнениям ангармонических упругих сред, описываемых мономиальными потенциалами. Обсуждается интегрируемость полученных уравнений и находятся некоторые их частные решения.Досліджується характер сил пружності, які задані нелінійними рівняннями релятивістських мембран та р-бран. Рівняння тороідальних бран перетворюються у класичні рівняння ангармонічних пружних середовищ, що описуються мономіальними потенціалами. Обговорюється інтегрування отриманих рівнянь. Знайдені їх деякі часткові рішення

Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained generalized supersymmetries admit a dual formulation. For both real and complex spinors generalized supersymmetries are constructed and classified as dimensional reductions of supersymmetries from {\em oxidized} space-times (i.e. the maximal space-times associated to $n$-component Clifford irreps). We apply these results to sistematically construct a class of models describing superparticles in presence of bosonic tensorial central charges, deriving the consistency conditions for the existence of the action, as well as the constrained equations of motion. Examples of these models (which, in their twistorial formulation, describe towers of higher-spin particles) were first introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and Lukierski (for complex spinors).Comment: 32 pages, LaTe

Hamiltonian structure and noncommutativity in pp-brane models with exotic supersymmetry

The Hamiltonian of the simplest super $p$-brane model preserving 3/4 of the D=4 N=1 supersymmetry in the centrally extended symplectic superspace is derived and its symmetries are described. The constraints of the model are covariantly separated into the first- and the second-class sets and the Dirac brackets (D.B.) are constructed. We show the D.B. noncommutativity of the super $p$-brane coordinates and find the D.B. realization of the $OSp(1|8)$ superalgebra. Established is the coincidence of the D.B. and Poisson bracket realizations of the $OSp(1|8)$ superalgebra on the constraint surface and the absence there of anomaly terms in the commutation relations for the quantized generators of the superalgebra.Comment: Latex, 27 pages, no figures. Latex packages amsfonts and euscript are use

Strings in a 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 $X^{\cal M}=(x^{m},z^{mn})$ with $z_{mn}$ describing a spin wave process. A supersymmetric version of the proposed model is formulated.Comment: 10 pages, Latex, style file espcrc2.sty. Talk given by AZ at the D.V. Volkov Memorial Conference ``Supersymmetry and Quantum Field Theory'', July 25-30, 2000, Kharkov, to be published in the Nuclear Physics B Conference Supplement