Abstract
We prove a generalised Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around $AdS_{d+1}$ with the aforementioned spectrum of fields, and a free $CFT_d$ of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.
Highlights
Existence of extended nonlinear higher-spin theories in AdSd+1, where mixed-symmetry fields, on top of the totally-symmetric ones, are propagating, together with some massive p-forms
Gauge fields always turned out to be of crucial importance, thereby it can be suspected that partially-massless field could be relevant in a unified framework for fundamental interactions, e.g. in a cosmological scenario [20] around dSd+1 where they are unitary
In [14], a version of higher-spin holography was proposed where a vector model at an isotropic Lifshitz fixed point is conjectured to be dual to a higher-spin gravity with spectrum given by a tower of massless and partially massless fields of unbounded integer spins — see [21] for a review of the conjecture
Summary
We spell out the approach that we followed in order to compute characters of so(2, d) and their fusion rules. The computation of the characters of the highest-weight representations we are interested in proceeds following a three-step procedure:. (1) We use the method explained in [12] to compute the character of a Verma module. We apply on it the so(d) Weyl group symmetrizer in order to obtain the character of the corresponding generalised Verma module;. For all the highest-weights we consider in detail, there is only one submodule which happens to be a generalised Verma module. The character of the latter is computed following the step 1;. The character of an irreducible representation of so(d) with dominantintegral weight s is denoted by χ(sd)(x1, . The weights (s1, . . . , sj, 1, . . . , 1, sj+m+1, . . . , sr) will be denoted (s1, . . . , sj, 1m, m sj+m+1, . . . , sr)
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