How massless are massless fields in $AdS_d$

TL;DR

This paper investigates the nature of massless fields with Young symmetry in AdS space, revealing that their degrees of freedom differ from flat space and proposing a pattern for their flat limit behavior.

Contribution

It demonstrates that AdS massless mixed symmetry fields decompose into multiple irreps of o(d-2), unlike in flat space, and proposes a general pattern for their flat space limit.

Findings

AdS massless fields reduce to multiple flat space irreps.

Not all flat space massless fields can be deformed to AdS with the same degrees of freedom.

The three-cell hook example shows only specific combinations admit smooth AdS deformation.

Abstract

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 massless field in flat space admits a deformation to $AdS_d$ with the same number of degrees of freedom, because it is impossible to keep all of the flat space 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 pattern 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 flat-space field with a graviton-like field admits a smooth deformation to $AdS_d$.