Higher spins dynamics in the closed string theory

TL;DR

This paper proposes a string action framework incorporating higher spin fields, derives their equations from quantum invariance, and analyzes the structure and equations at the first massive level of closed bosonic strings.

Contribution

It introduces a sigma-model approach for higher spin backgrounds in string theory and derives their field equations from quantum Weyl invariance, with detailed analysis at the first massive level.

Findings

Renormalization can be performed level by level.

Field equations for higher spin backgrounds are derived from invariance conditions.

Detailed structure of background fields at the first massive level is provided.

Abstract

The general $\sigma$-model-type string action including both massless and massive higher spins background fields is suggested. Field equations for background fields are followed from the requirement of quantum Weyl invariance. It is shown that renormalization of the theory can be produced level by level. The detailed consideration of background fields structure and corresponding fields equations is given for the first massive level of the closed bosonic string.