Gauge-invariant description of massive higher-spin particles by dimensional reduction

Abstract

We study the dimensional reduction of free massless higher-spin theories from five dimensions to four-dimensional space-time. The fifth dimension is assumed to be compactified to a circle of radius 1/m. For spin s, the resulting four-dimensional theory describes massless fields of spin s, s-1, s-2,..., together with an infinite number of massive fields of spin s. These correspond to a member of a class of theories given by Zinoviev which are gauge-invariant descriptions of massive higher-spin particles. We show that in our theory massive modes have gauge invariance associated with them. We also show that Schwinger’s source constraints are obtained as source constraints due to gauge invariance. These results have been shown for spins s=1, (3/2), 2, and (5/2). We also discuss in the context of our work interacting higher-spin theories and Fronsdal’s source constraints for a smooth massless limit.