On quantum corrections in higher-spin theory in flat space

TL;DR

We analyze a flat-space theory of an infinite tower of massless higher-spin fields with cubic vertices fixed by Metsaev, controlled by a dimensionless coupling $g$ and a length scale $ell$. We compute the one-loop scalar self-energy by summing over all higher-spin loops and find an exponential UV divergence that could be cancelled by a tadpole from an as-yet-undetermined quartic vertex, while the tree-level 4-scalar amplitude from higher-spin exchanges shows exponential growth in the high-energy limit. We also show that the covariant cubic vertices fail the BCFW four-particle test, indicating potential issues with constructibility in this non-local setup, and discuss possible parallels with AdS/CFT where symmetry may force vanishing loop corrections. The work highlights the critical role of the quartic vertex and the full non-local action for UV behavior and motivates further study of flat-space higher-spin interactions and their AdS counterparts.

Abstract

We consider an interacting theory of an infinite tower of massless higher-spin fields in flat space with cubic vertices and their coupling constants found previously by Metsaev. We compute the one-loop bubble diagram part of the self-energy of the spin 0 member of the tower by summing up all higher-spin loop contributions. We find that the result contains an exponentially UV divergent part and we discuss how it could be cancelled by a tadpole contribution depending on yet to be determined quartic interaction vertex. We also compute the tree-level four-scalar scattering amplitude due to all higher-spin exchanges and discuss its inconsistency with the BCFW constructibility condition. We comment on possible relation to similar computations in AdS background in connection with AdS/CFT.