Supersymmetric Lorentz invariant deformations of superspaces

Abstract

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor ${\lambda }_a$ and Ramond grassmannian vector ${\psi }_m=-\frac{1}{2}(\bar{\theta }{\gamma }_m\lambda )$ in the spinor realization \cite{VZ} are proposed. The map of supergravity background into composite supercoordinates: $(B_{mn}^{-1},{\Psi }_m^a,C_{ab})\leftrightarrow (i{\psi }_m{\psi }_n,{\psi }_m{\lambda }^a,{\lambda }_a{\lambda }_b)$ valid up to the second order corrections in deformation parameter $h$ and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordinates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector ${\psi }_{1m}=1/2(\bar{\theta }{\gamma }_m{\gamma }_5\lambda )$ and to vanish for the $\theta$ components with the same chiralities. The deformations in the (super)twistor picture are discussed.

Latex, 13 pages, no figures; Talk at the Conference ``Cosmology 2005: a reality check'', December 14-17, 2005, Copenhagen, Denmark; To appear at http://www.astro.ku.dk/dark/workshops/dark05/presentations.html

References in corpus (7)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Non-commutative superspace from string theory
• Gravity Induced C-Deformation
• Wess-Zumino actions and Dirichlet Boundary Conditions for Super p-branes with Exotic Fractions of Supersymmetry
• Quantum BRST charge and OSp(1|8) superalgebra of twistor-like p-branes with exotic supersymmetry and Weyl symmetry

Cited by in corpus (7)

• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• On the cancellation of 4-derivative terms in the Volkov-Akulov action
• Nilpotent noncommutativity and renormalization
• Unification of twistors and Ramond vectors
• A new type of supersymmetric twistors and higher spin chiral multiplets
• Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor
• The $\theta$-twistor versus the supertwistor