String theory triplets and higher-spin curvatures

TL;DR

The work investigates unconstrained higher-spin gauge theories emerging from the tensionless limit of open string field theory by recasting triplet Lagrangians in a geometric curvature language. By integrating out auxiliary fields, it derives local effective Lagrangians for both bosonic and fermionic symmetric fields that can be written as curvature-squared or curvature-divergence terms, i.e., as Maxwell-like expressions in terms of higher-spin curvatures $\mathcal{R}^{(s)}$. The main contributions are explicit curvature-based forms for the bosonic and fermionic effective actions and their equations of motion, showing that higher-spin curvatures can encode dynamics even without the Fronsdal-Labastida constraints. The results suggest a curvature-driven perspective on interacting higher-spin theories and may offer a route to deform nonlocal curvature theories into local, auxiliary-field formulations.

Abstract

Unconstrained local Lagrangians for higher-spin gauge theories are bound to involve auxiliary fields, whose integration in the partition function generates geometric, effective actions expressed in terms of curvatures. When applied to the triplets, emerging from the tensionless limit of open string field theory, the same procedure yields interesting alternative forms of geometric Lagrangians, expressible for both bosons and fermions as squares of field-strengths. This shows that higher-spin curvatures might play a role in the dynamics, regardless of whether the Fronsdal-Labastida constraints are assumed or forgone.