Higher Spins at the Quintic Order: Localization Effect and Simplifications

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 $s_4=4$