AdS3/AdS2 degression of massless particles

We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS(3) space foliated into AdS(2) hypersurfaces. It is shown that an AdS(3) massless particle of spin s = 1, 2, horizontal ellipsis , infinity degresses into a couple of AdS(2) particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS(3)/AdS(2) degression we consider branching rules for AdS(3) isometry algebra o(2,2) representations decomposed with respect to AdS(2) isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.