Shift Symmetries in (Anti) de Sitter Space

Abstract

We construct a class of extended shift symmetries for fields of all integer spins in de Sitter (dS) and anti-de Sitter (AdS) space. These generalize the shift symmetry, galileon symmetry, and special galileon symmetry of massless scalars in flat space to all symmetric tensor fields in (A)dS space. These symmetries are parametrized by generalized Killing tensors and exist for fields with particular discrete masses corresponding to the longitudinal modes of massive fields in partially massless limits. We construct interactions for scalars that preserve these shift symmetries, including an extension of the special galileon to (A)dS space, and discuss possible generalizations to interacting massive higher-spin particles.

54 pages, 4 figures. v3 several more typos corrected

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• A note on the representations of $\text{SO}(1,d+1)$
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• An Algebraic Classification of Exceptional EFTs
• The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales
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• Symmetric Scalars
• Soft limits of the wavefunction in exceptional scalar theories
• A theory for multiple partially massless spin-2 fields
• Shift-Symmetric Spin-1 Theories
• $\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS
• An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry
• Shift Symmetries and AdS/CFT
• Scale and Conformal Invariance on (A)dS
• Fermionic Shift Symmetries in (Anti) de Sitter Space
• Inequivalent Goldstone Hierarchies for Spontaneously Broken Spacetime Symmetries
• On the Conformal Symmetry of Exceptional Scalar Theories
• On the EFT of Conformal Symmetry Breaking
• Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Fractonic Coset Construction for Spontaneously Broken Translations
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• De Sitter Horizon Edge Partition Functions
• Real-time observables in de Sitter thermodynamics
• Equivalence of EFTs and Time-Like Extra Dimensions
• Gravitons on Nariai Edges
• New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation
• Soft unification of exceptional effective field theories in de Sitter space
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes