Unitarity in three-dimensional flat space higher spin theories

Abstract

We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean $W_4^{(2-1-1)}$ algebra. We extend this no-go result to rule out unitary "multi-graviton" theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.

arXiv comment34 pp, v2: added two paragraphs in section 5.3 + minor changes

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Cited by in corpus (16)

• Tensionless Strings from Worldsheet Symmetries
• BMS Modules in Three Dimensions
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Flat space (higher spin) gravity with chemical potentials
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Flat Space Limit of (Higher-Spin) Cardy Formula
• Rotating Higher Spin Partition Functions and Extended BMS Symmetries
• Semi-classical BMS${}_3$ blocks and flat holography
• Spectral Flow in 3D Flat Spacetimes
• Free-field realisations of the BMS${}_3$ algebra and its extensions
• BMS Characters and Modular Invariance
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Unfolded Fierz-Pauli Equations in Three-Dimensional Asymptotically Flat Spacetimes
• Free-field construction of Carrollian $W_N$-algebras