Metric- and frame-like higher-spin gauge theories in three dimensions

Abstract

We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like formulation. The metric-like theory is obtained by eliminating the generalised spin connection by its equation of motion, and by expressing everything in terms of the metric and a spin-3 Fronsdal field. We give an exact map between fields and gauge parameters in both formulations. To work out the gauge transformations explicitly in terms of metric-like variables, we have to make a perturbative expansion in the spin-3 field. We describe an algorithm how to do this systematically, and we work out the gauge transformations to cubic order in the spin-3 field. We use these results to determine the gauge algebra to this order, and explain why the commutator of two spin-3 transformations only closes on-shell.

arXiv comment26 pages, no figures

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Cited by in corpus (15)

• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• New Conformal Higher Spin Gravities in $3d$
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• Cubic interactions of massless bosonic fields in three dimensions
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• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Cubic interactions of arbitrary spin fields in 3d flat space
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• Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Frame- and Metric-like Higher-Spin Fermions
• Higher spin JT gravity and a matrix model dual
• Connection vs metric description for non-AdS solutions in higher spin theories
• Quasi-Local Conserved Charges of Spin-3 Topologically Massive Gravity
• Reformulations of Yang-Mills Theories with Space-time Tensor Fields