On Singleton Composites in Non-compact WZW Models

TL;DR

This paper explores the structure and representations of a specific non-compact WZW model related to the scalar singleton in AdS space, revealing new insights into its algebraic properties and potential links to higher-spin theories.

Contribution

It introduces a novel analysis of the so(2,D-1) WZW model at subcritical level, detailing its vacuum structure, representations, and connections to singleton particles and higher-spin theories.

Findings

Identifies the singular vacuum vector at Virasoro level 2.

Describes the spectrum including singletons and their composites.

Proposes links to phase-space quantization and higher-spin gauge theories.

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.