We analyze the Weyl invariance constraints on higher spin vertex operators in open superstring theory describing massless higher spin gauge field excitations in $d$-dimensional space-time. We show that these constraints lead to low-energy equations of motion for higher spin fields in AdS space, with the leading-order $\beta$ function for the higher spin fields producing Fronsdal’s operator in ${\mathrm{AdS}}_{d+1}$, despite that the higher spin vertex operators are originally defined in flat background. The correspondence between the $\beta$ function in string theory and ${\mathrm{AdS}}_{d+1}$ Fronsdal operators in space-time is found to be exact for $d=4$, while for other space-time dimensions, it requires modifications of manifest expressions for the higher spin vertex operators. We argue that the correspondence considered in this paper is the leading order of a more general isomorphism between Vasiliev’s equations and equations of motion of extended open string field theory, generalized to include the higher spin operators.

• Received 4 September 2013

DOI:https://doi.org/10.1103/PhysRevD.89.026010