Dmitrij V. Volkov

From the superparticle Siegel symmetry to the spinning particle proper-time supersymmetry

Abstract The classical equivalence between the lagrangians of the N=1, D=10 massless superparticle and spinning particle is established. This is done by fixing the gauge of seven independent Siegel transformations, identifying the remaining Lorentz-covariant Siegel generator with that of n=1 local proper-time supersymmetry of the spin 1 2 particle and redefining the superparticle fermionic degrees of freedom by means of a generalized twistor-like approach.

On the relationship between compactified vacua of d = 11 and d = 10 supergravities

Abstract It is shown that the Freund-Rubin vacuum configurations of d = 11 supergravity can be identified with corresponding vacua of non-chiral N = 2, d = 10 supergravity by considering the compact subspaces M 7 of the d = 11 theory as fibre bundles P(M 6 ,S 1 ) with the base spaces M 6 , being the solutions of the N = 2, d = 10 equations of motion. But in spite of this correspondence between vacuum configurations of the two theories,in N = 2, d = 10 supergravity only backgrounds with M 6 =T 6 , SU(4)/U(3), K 3 × T 2 , S p (2)/(S p (1)×U(1)), SU(3)/(U(1)×U′(1)) admit supersymmetry convervation in the effective d = 4 theory with only N = 8,6,4,1 supersymmetries being conserved.

Lagrangians for massless particles and strings with local and global supersymmetry

Abstract A superfield approach to the description of massless particles and strings lagrangians invariant under local (world-sheet) and global (space-time) supersymmetries is developed. The equivalency between the lagrangians of spinning and supersymmetrical particles presented in terms of u A and θ A Weyl spinor variables is established. It is shown that the condition of the inverse Higgs effect for the Grassmann invariant superform leads to the realization of dynamical variables by means of commuting space Weyl spinors u A for massless particles and commuting space Weyl and world-sheet spinors u Aα for strings. A new model of fermionic superstrings is suggested.

Anti) commuting spinors and supersymmetric dynamics of semions

Abstract A twistor-like formulation of the classical dynamics of free massive particles is proposed which upon quantization results in semion states with helicities s = 1 2 ( 1 2 +n) . A space-time supersymmetric generalization of the model allows one to treat the fields with helicities differing by 1 2 on an equal footing as the components of a single superfield, thus, attributing to them the relative Grassmann statistics. Supersymmetric equations for semions with the helicity 1 4 and 3 4 are obtained and a corresponding local superfield action for a Grassmann semion superfield is constructed.

Doubly supersymmetric null strings and string tension generation

Abstract We propose a twistor-like formulation of N = 1, D = 3, 4, 6 and 10 null superstrings. The model possesses N = 1 target space supersymmetry and n = D − 2 local worldsheet supersymmetry, the latter replaces the κ-symmetry of the conventional approach to the strings. Adding a Wess-Zumino term to a null superstring action we observe a string tension generation mechanism [J.A. De Azcarraga, J.M. Izquierdo and P.K. Townsend, Phys. Rev. D 45 (1992) 3321; P.K. Townsend, Phys. Lett. B 277 (1992) 285; E. Bergshoeff, L.A.J. London and P.K. Townsend, Class. Quantum Grav. 9 (1992) 2545; and F. Delduc, A. Galperin, P. Howe and E. Sokatchev, Phys. Rev. D 47 (1992) 578]: the induced worldsheet metric becomes nondegenerate and the resulting model turns out to be classically equivalent to the heterotic string.

New supersymmetric generalization of the Liouville equation

Abstract We present n = (1,1) and n = (1,0) supersymmetric generalization of the Liouville equation which originate from a geometrical approach to describing the classical dynamics of Green-Schwarz superstrings in N = 2, D = 3 and N = 1, D = 3 target superspace. Considered are a zero curvature representation and Backlund transformations associated with the supersymmetric non-linear equations.

Supergravity Before 1976

A story on how an attempt to realize W. Heisenberg’s idea that the neutrino might be a Goldstone particle had led in its development to the discovery of a supergravity action. 1. Introduction 2. Goldstone fermions, super-Poincare group and its spontaneous breaking 3. Gauged super-Poincare group 4. Supergravity action and super-Higgs effect 5. Superspace formulation of Supergravity (first steps into Superspace) 6. Resume

A generalized twistor dynamics of relativistic particles and strings

A generalization of relativistic particle and string dynamics based on a notion of twistor shift and containing a fundamental length constant is considered, which results in a modification of particle (or string) interactions with background fields.

D = (0|2) DIRAC–MAXWELL–EINSTEIN THEORY AS A WAY FOR DESCRIBING SUPERSYMMETRIC QUARTIONS

Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin 1/4 and 3/4 (quartions), where the role of quartion momentum in effective (2+1)--dimensional space-time is played by an abelian gauge superfield propagating in a basic two-dimensional Grassmann-odd space with a cosmological constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd) dimensional model of quartions interacting with the gauge and gravitational field manifests itself as an effective (2+1)-dimensional supersymmetric theory of free quartions.

Twistors and Supersymmetry

In modern theoretical physics there are two branches of research which are closely related to fundamental problems of space-time. These are twistors and supersymmetry. Recently a growing tendency to intertwining these two branches has been appearing, and it is now widely believed that twistors may play an essential part in the foundation of supersymmetric theories. The main point where twistors and supersymmetry are in touch is the integrability conditions for N-extended and D = 10 super Yang-Mills theories and supergravity which, in its turn, is connected with the fact that the trajectory of a massless superparticle in superspace is not a world line but a supersurface with one bosonic and a number of fermionic directions.