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 \( {\mathcal{W}}_4^{\left(2-1-1\right)} \) 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.
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Grumiller, D., Riegler, M. & Rosseel, J. Unitarity in three-dimensional flat space higher spin theories. J. High Energ. Phys. 2014, 15 (2014). https://doi.org/10.1007/JHEP07(2014)015
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DOI: https://doi.org/10.1007/JHEP07(2014)015