Generalised connections and higher-spin equations

Understand

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.