Chiral Tensors of Mixed Young Symmetry

Abstract

Chiral tensors of mixed Young symmetry, which exist in the same spacetime dimensions $2+4n$ where chiral $p$-forms can be defined, are investigated. Such chiral tensors have been argued to play a central role in exotic formulations of gravity in 6 dimensions and possess intriguing properties. A variational principle that yields the chiral equations of motion is explicitly constructed and related to the action for a non-chiral tensor. The use of prepotentials turns out to be essential in our analysis. We also comment on dimensional reduction.

Expanded version with 3 appendices providing explicit proofs of central results

References in corpus (6)

• Off-shell massive N=1 supermultiplets in three dimensions
• Higher spin super-Cotton tensors and generalisations of the linear-chiral duality in three dimensions
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Twisted self-duality for higher spin gauge fields and prepotentials
• Supersymmetric electric-magnetic duality of hypergravity
• A deformation of the Curtright action

Cited by in corpus (15)

• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Toward Exotic 6D Supergravities
• Fermionic Higher-form Symmetries
• A note on the double dual graviton
• Unified non-metric (1,0) tensor-Einstein supergravity theories and (4,0) supergravity in six dimensions
• Symmetrization of Jordan dialgebras
• The Magic Star of Exceptional Periodicity
• The Mile High Magic Pyramid
• The Action of the (free) $(4,0)$-theory
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• Prepotentials for linearized supergravity
• Spin-2 twisted duality in (A)dS
• Massless chiral fields in six dimensions
• Aspects of electric-magnetic dualities in maximal supergravity
• Duality Anomalies in Linearized Gravity