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.
Highlights
Necessarily imply that the theory is trivial; in particular in the presence of a boundary, boundary states that lie in a representation of a non-trivial asymptotic symmetry algebra can exist
We showed by examples and by a general no-go result that for standard definitions of the vacuum and adjoint operators flat space higher spin gravity is incompatible with unitarity
Phrased differently, imposing unitarity leads to a further contraction of the asymptotic symmetry algebra that decouples all higher-spin states from the physical spectrum
Summary
We summarize known facts about flat space contractions and unitarity. In subsection 2.1 we review aspects of 3-dimensional flat space holography for spin-2 theories,. Following Bagchi et al, and Barnich et al In subsection 2.2 we comment on unitarity for Galilean conformal algebras. In subsection 2.3 we collect some of the main results for the Inonu-Wigner contraction of higher spin gravity for the principal embedding [5, 6]
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