New Conformal Higher Spin Gravities in $3d$

Abstract

We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new theories with a finite number of higher spin fields, much as in the massless case. The action has the Chern-Simons form for a higher spin extension of the conformal algebra. In general, the new theories contain Fradkin-Tseytlin fields with higher derivatives in the gauge transformations, which is reminiscent of partially-massless fields. A relation of the old and new theories to the parity anomaly is pointed out.

arXiv comment20 pages+refs; replaced with the journal version

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Cited by in corpus (31)

• More on Quantum Chiral Higher Spin Gravity
• Actions for Self-dual Higher Spin Gravities
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• One-loop Finiteness of Chiral Higher Spin Gravity
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Toward a twistor action for chiral higher-spin gravity
• Higher-Spin Self-Dual Yang-Mills and Gravity from the twistor space
• Minimal models of field theories: Chiral Higher Spin Gravity
• Higher-spin Yang-Mills, amplitudes and self-duality
• Minimal model of Chiral Higher Spin Gravity
• Towards higher-spin AdS${}_2$/CFT${}_1$ holography
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Chiral Higher Spin Gravity and Convex Geometry
• Cubic interactions of arbitrary spin fields in 3d flat space
• A Stringy theory in three dimensions and Massive Higher Spins
• A Twistorial Description of the IKKT-Matrix Model
• On BF-type higher-spin actions in two dimensions
• Higher-spin gauge theories in three spacetime dimensions
• Constraining higher-spin S-matrices
• Generalised superconformal higher-spin multiplets
• Generalised conformal higher-spin fields in curved backgrounds
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Hypergravity in five dimensions
• Infinite distances in multicritical CFTs and higher-spin holography
• 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
• Conformal Galilean Spin-3 Gravity in 3d
• Conformal Carrollian Spin-3 Gravity in 3d
• Consistent deformations in the presymplectic BV-AKSZ approach
• Enhanced Conformal $BM{S}_3$ Symmetries