On the geometry of higher-spin gauge fields

We review a recent construction of the free-field equations for totally symmetric tensors and tensor-spinors that exhibits the corresponding linearized geometry. These equations are not local for all spins >2, involve unconstrained fields and gauge parameters, rest on the curvatures introduced long ago by de Wit and Freedman and reduce to the local (Fang-)Fronsdal form upon partial gauge fixing. We also describe how the higher-spin geometry is realized in free string field theory, and how the gauge fixing to the light cone can be effected.