Higher Spins at the Quintic Order: Localization Effect and Simplifications

TL;DR

This paper explores the quintic interactions of massless higher spin gauge fields using string theory, revealing significant simplifications and localization effects under specific spin constraints and configurations.

Contribution

It provides explicit calculations of the 5-point interaction vertex for higher spins, demonstrating conditions that lead to simplified and localized interaction structures.

Findings

Interaction structure simplifies under specific spin sum constraints

Localization effects occur when one spin value is small

Explicit 5-point vertex computed for a case with s_4=4

Abstract

We investigate the special case of quintic interactions for massless higher spin gauge fields using the string-theoretic vertex operator construction for higher spin gauge fields in Vasiliev's frame-like formalism. We compute explicitly the related 5-point interaction vertex in the low energy limit of string theory and find that: the structure of the quintic $s_1-s_2-s_3-s_4-s_5$ higher spin interaction gets drastically simplified and localized if a) the spin values satisfy the constraint $s_1+s_2+s_3=s_4+s_5+2$ (and, more generally, if the sum of three spin values roughly equals the sum of the remaining two b) One of the spin values, $s_4$ or $s_5$ is sufficiently small. In this paper, the explicit computation is done for the case $s_4=4$