### Abstract

We consider a minimal interacting theory of a single tower of spin j = 0, 2, 4,… massless Fronsdal fields in flat space with local Lorentz-covariant cubic interaction vertices. We address the question of constraints on possible quartic interaction vertices imposed by the condition of on-shell gauge invariance of the tree-level four-point scattering amplitudes involving three spin 0 and one spin j particle. We find that these constraints admit a local solution for quartic 000j interaction term in the action only for j = 2 and j = 4. We determine the non-local terms in four-vertices required in the j ≥ 6 case and suggest that these non-localities may be interpreted as a result of integrating out a tower of auxiliary ghost-like massless higher spin fields in an extended theory with a local action, up to possible higher-point interactions of the ghost fields. We also consider the conformal off-shell extension of the Einstein theory and show that the perturbative expansion of its action is the same as that of the non-local action resulting from integrating out the trace of the graviton field from the Einstein action. Motivated by this example, we conjecture the existence of a similar conformal off-shell extension of a massless higher spin theory that may be related to the above extended theory. It may then have the same infinite-dimensional symmetry as the higher-derivative conformal higher spin theory and may thus lead to a trivial S matrix.

Original language | English (US) |
---|---|

Article number | 139 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2017 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Fingerprint Dive into the research topics of 'On four-point interactions in massless higher spin theory in flat space'. Together they form a unique fingerprint.

## Cite this

*Journal of High Energy Physics*,

*2017*(4), [139]. https://doi.org/10.1007/JHEP04(2017)139