How massless are massless fields in AdS(d)

Massless fields of generic Young symmetry type in AdS(d) space are analyzed . It is demonstrated that in contrast to massless fields in Minkowski space whose physical degrees of freedom transform in irreps of o(d - 2) algebra, AdS massless mixed symmetry fields reduce to a number of irreps of o(d - 2 ) algebra. From the field theory perspective this means that not every mass less field in flat space admits a deformation to AdS(d) with the same numbe r of degrees of freedom, because it is impossible to keep all of the flat s pace gauge symmetries unbroken in the AdS space. An equivalent statement is that, generic irreducible AdS massless fields reduce to certain reducible sets of massless fields in the flat limit. A conjecture on the general patt ern of the flat space limit of a general AdS(d) massless field is made. The example of the three-cell "hook" Young diagram is discussed in detail. In particular, it is shown that only a combination of the three-cell fiat-spac e field with a graviton-like field admits a smooth deformation to AdS(d). ( C) 2000 Elsevier Science B.V. All rights reserved.