Generalised connections and higher-spin equations

TL;DR

This paper explores high-derivative higher-spin equations derived from curvature divergences, showing their equivalence to tensionless string theory equations and expanding the understanding of higher-spin field equations.

Contribution

It introduces a systematic analysis of high-derivative equations from higher-spin curvatures, linking them to tensionless string field theory and extending the framework of higher-spin equations.

Findings

High-derivative equations are equivalent to tensionless string equations.

Divergences of higher-spin curvatures produce a systematic pattern of equations.

The approach complements existing methods based on trace conditions.

Abstract

We consider high-derivative equations obtained setting to zero the divergence of the higher-spin curvatures in metric-like form, showing their equivalence to the second-order equations emerging from the tensionless limit of open string field theory, which propagate reducible spectra of particles with different spins. This result can be viewed as complementary to the possibility of setting to zero a single trace of the higher-spin field strengths, which yields an equation known to imply Fronsdal's equation in the compensator form. Higher traces and divergences of the curvatures produce a whole pattern of high-derivative equations whose systematics is also presented.