Aleksandr A. Zheltukhin

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 zmn 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 zmn to one real effective coordinate which composes an effective 5-dimensional target space together with the xm 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 -matrix of the P.B. of the second class constraints is constructed and its algebraic structure is further presented.

Exactly solvable p-brane model with extra supersymmetry

Abstract 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.

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

Abstract String dynamics in a curved space-time is studied on the basis of an action functional including the small parameter of rescaled tension e = γ / α ′, where γ is a metric parametrizing constant. A rescaled slow world-sheet time T = eτ is introduced, and general covariant non-linear string equations are derived. It is shown that in the first order of an e-expansion these equations are reduced to the known equation for geodesic deviation 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 ( α ′ H 2 ⪢ 1).

Exact solutions for U(1) globally invariant membranes

Abstract The exact solvability problem of the nonlinear equations describing the U ( 1 ) invariant membranes is studied and the general solution for the static membrane in D = ( 2 N + 1 ) -dimensional Minkowski space–time, including M-theory case D = 11 , is obtained. The D = 5 time-dependent elliptic cosine solution describing a family of contracting tori is also found, together with the solution corresponding to a spinning torus characterized by the presence of the critical rotation frequency Ω max = T 1 / 3 π expressed via the membrane tension T.

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

Abstract 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 (1,2 M ) 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 (1,2 M )-invariant super p -brane and D p -brane-like actions preserving ( 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.

Extra gauge symmetry for extra supersymmetry

Abstract 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 κ -symmetry. It is proved that the composed gauge invariant coordinates coincide with the components of symplectic supertwistor realizing a linear representation of the hidden OSp (1,2 M ) 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.

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

Abstract Exact solvability of brane equations is studied, and a new U ( 1 ) × U ( 1 ) × ⋯ × U ( 1 ) invariant anzats for the solution of p-brane equations in D = ( 2 p + 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.

Cancellation of 4-derivative terms in Volkov-Akulov action

Recently Kuzenko and McCarty observed the cancellation of 4derivative terms in the D = 4 N = 1 Volkov-Akulov supersymmetric action for the fermionic Nambu-Goldstone field. Here is presented a simple algebraic proof of the cancellation based on using the Majorana bispinors and Fierz identities. The cancellation shows a difference between the Volkov-Akulov action and the effective superfield action recently studied by Komargodski and Seiberg and containing one 4derivative term. We find out that the cancellation effect takes place in coupling of the Nambu-Goldstone fermion with the Dirac field. Equivalence between the KS and the VA Lagrangians is proved up to the first order in the interaction constant of the NG fermions.

Dmitrij Volkov, super‐Poincaré group and Grassmann variables

A fundamental role of the Hermann Grassmann anticommuting variables both in physics and mathematics is discussed on the example of supersymmetry. The talk describes how the D. Volkov question about possibility of the existence of Nambu-Goldstone fermions, realized by the Grassmannian variables, resulted in the discovery of the super-Poincare group, its spontaneous breaking and gauging.

Unification of twistors and Ramond vectors

Abstract We generalize the idea of supertwistors and introduce a new supersymmetric object—the θ-twistor which includes the composite Ramond vector [D.V. Volkov, A.A. Zheltukhin, JETP Lett. 48 (1988) 63] well known from the spinning string dynamics. The symmetries of the chiral θ-twistor superspace are studied. It is shown that the chiral spin structure introduced by the θ-twistor breaks the superconformal boost symmetry but preserves the scale symmetry and the super Poincare symmetry. This geometrical effect of breaking correlates with the Gross–Wess effect of the conformal boost breaking for bosonic scattering amplitudes.