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arXiv · hep-th/0701163

Current Exchanges and Unconstrained Higher Spins

D. Francia·J. Mourad·A. Sagnotti
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Abstract

The (Fang-)Fronsdal formulation for free fully symmetric (spinor-) tensors rests on (gamma-)trace constraints on gauge fields and parameters. When these are relaxed, glimpses of the underlying geometry emerge: the field equations extend to non-local expressions involving the higher-spin curvatures, and with only a pair of additional fields an equivalent ``minimal'' local formulation is also possible. In this paper we complete the discussion of the ``minimal'' formulation for fully symmetric (spinor-) tensors, constructing one-parameter families of Lagrangians and extending them to (A)dS backgrounds. We then turn on external currents, that in this setting are subject to conventional conservation laws and, by a close scrutiny of current exchanges in the various formulations, we clarify the precise link between the local and non-local versions of the theory. To this end, we first show the equivalence of the constrained and unconstrained local formulations, and then identify a unique set of non-local Lagrangian equations which behave in exactly the same fashion in current exchanges.

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D. Francia, J. Mourad, A. Sagnotti. 2007-03-25. Current Exchanges and Unconstrained Higher Spins. https://doi.org/10.1016/j.nuclphysb.2007.03.021

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