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.

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

References in corpus (9)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Galilean Conformal Algebras and AdS/CFT
• Symmetries of Holographic Minimal Models
• Entropy of three-dimensional asymptotically flat cosmological solutions
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Cited by in corpus (7)

• 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
• Spectral Flow in 3D Flat Spacetimes
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories