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arXiv · 1702.00222

On induced action for conformal higher spins in curved background

M. Beccaria·A. A. Tseytlin
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Abstract

We continue the investigation of the structure of the action for a tower of conformal higher spin fields in non-trivial 4d background metric recently discussed in arXiv:1609.09381. The action is defined as an induced one from path integral of a conformal scalar field in curved background coupled to higher spin fields. We analyse in detail the dependence of the quadratic part of the induced action on the spin 1 and spin 3 fields, determining the presence of a curvature-dependent mixed spin 1 - spin 3 term. One consequence is that the pure spin 3 kinetic term cannot be gauge-invariant on its own beyond the leading term in small curvature expansion. We also compute the non-zero contribution of the 1-3 mixing term to the conformal anomaly c-coefficient. One is thus to determine all such mixing terms before addressing the question of possible vanishing of the total c-coefficient in the conformal higher spin theory.

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M. Beccaria, A. A. Tseytlin. 2017-10-24. On induced action for conformal higher spins in curved background. https://doi.org/10.1016/j.nuclphysb.2017.03.022

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