On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field

Abstract

We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. Both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. Explicit expressions for the source terms are suggested and subjected to some simple tests. We also discuss a cascading relation between the Chern-Simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 Chern-Simons action in terms of the spin connection expressed in terms of the frame field. This cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.

v2: 20 pages, misprints corrected, footnotes added

References in corpus (3)

• Three-dimensional N=8 conformal supergravity and its coupling to BLG M2-branes
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Critical solutions in topologically gauged N=8 CFTs in three dimensions

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• Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space
• Topologically massive higher spin gauge theories
• Twisted self-duality for higher spin gauge fields and prepotentials
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• All-Order Quartic Couplings in Highly Symmetric D-brane-Anti-D-brane Systems