Universal structure in the interactions of massless fields on the light cone

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Abstract
We consider cubic interactions of massless fields of arbitrary spin in four spacetime dimensions, within the light cone formalism. We extend two key results from flat to (anti-)de Sitter spacetime. First, we present a simple explicit expression for all the cubic vertices. Second, we prove that the various self-dual/chiral theories, such as self-dual Yang-Mills, self-dual general relativity, and chiral higher-spin gravity, are fully consistent with no need for vertices beyond cubic. The key observation behind our results is that all cubic vertices in the light cone formalism can be expressed as a direct generalization of the “Abelian” vertices formed by multiplying linearized curvatures. The simple relationship between flat and (anti-)de Sitter then follows essentially from the conformal invariance of such linearized curvatures. The price for such simplicity is that our vertex expressions are nonlocal. It is, however, easy to bring them into a local form, which we also present.
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  • Okinawa Institute of Science and Technology Graduate University

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