The off-shell behavior of propagators and the Goldstone field in higher spin gauge theory on AdSd+1 space

A detailed analysis of the structure and gauge dependence of the bulk-to-bulk propagators for the higher spin gauge fields in AdS space is performed. The possible freedom in the construction of the propagators is investigated and fixed by the correct boundary behavior and correspondence to the representation theory results for the AdS space isometry group. The classical origin of the Goldstone mode and its connection with the gauge fixing procedure is considered.