Abstract
We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t ≤ s. In the case of the usual Fradkin-Tseytlin fields t = 1 this gives a systematic derivation of the factorization formulas known in the literature while for t > 1 the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.
Highlights
Wave operators for conformal higher spin (CHS) fields (CHS operators) are of order n − 4 + 2s and were conjectured [10] to factorize into a product of 2nd order operators when written over the constant curvature background
We study conformal higher spin (CHS) fields on constant curvature backgrounds
By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t s
Summary
In this work we are concerned with conformal gauge fields defined on the conformally-flat spaces. The conformal symmetry can be seen as originating from the conformal isometries which, at the infinitesimal level, are given by conformal Killing vector fields These form o(n, 2) algebra, where n is the space-time dimension. And in what follows · denotes o(n, 2)-invariant contraction of indices, e.g. Z · W = ηABZAW B and X2 = X · X Because both the constraint and the equivalence relation are manifestly o(n, 2)-invariant the conformal algebra act on the space defined by (2.2) (the same applies to the conformal group). If we restrict ourselves to totally symmetric fields it is convenient to work in terms of generating functions defined on the cotangent bundle over the ambient space. It is clear that E[w] is equipped with a natural action of o(n, 2) induced by that on the cotangent bundle over the ambient space
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