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arXiv · 1403.5297

Unitarity in three-dimensional flat space higher spin theories

D. Grumiller·M. Riegler·J. Rosseel
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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.

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D. Grumiller, M. Riegler, J. Rosseel. 2014-05-23. Unitarity in three-dimensional flat space higher spin theories. https://doi.org/10.1007/jhep07(2014)015

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