On Singleton Composites in Non-compact WZW Models

Abstract

We examine the so(2,D-1) WZW model at the subcritical level -(D-3)/2. It has a singular vacuum vector at Virasoro level 2. Its decoupling constitutes an affine extension of the equation of motion of the (D+1)-dimensional conformal particle, i.e. the scalar singleton. The admissible (spectrally flowed) representations contain the singleton and its direct products, consisting of massless and massive particles in AdS_D. In D=4 there exists an extended model containing both scalar and spinor singletons of sp(4). Its realization in terms of 4 symplectic-real bosons contains the spinor-oscillator constructions of the 4D singletons and their composites. We also comment on the prospects of relating gauged versions of the models to the phase-space quantization of partonic branes and higher-spin gauge theory.

41 pages; v2: a figure and one reference added

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Cited by in corpus (7)

• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• Flato-Fronsdal theorem for higher-order singletons
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• Twistor space observables and quasi-amplitudes in 4D higher spin gravity
• 2D sigma models and differential Poisson algebras
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Linearized Coxeter Higher-Spin Theories