Local cubic vertex functions for three massless higher even spin fields on spaces AdS_D: An analytic approach

TL;DR

This paper develops a covariant, analytic method to construct local cubic vertex functions for three massless higher even spin fields in AdS_D, linking conserved currents, gauge invariance, and UV divergences.

Contribution

It introduces a new analytic approach to derive local cubic vertices for higher spin fields in AdS, emphasizing covariance and the role of UV divergences.

Findings

Derived concise formulas for cubic vertex functions

Maintained covariance at all steps of the construction

Linked vertex functions to UV divergences in dimensional regularization

Abstract

Local cubic vertex functions of three higher even spin fields on AdS_D are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV divergence as the residue of the highest order pole in the dimensional regularization parameter \epsilon. The method works for even D and maintains covariance at any step. The resulting formula is quite concise.