paper

Higher-spin massless S-matrices in four-dimensions

arXiv:1311.2938 · doi:10.1103/PhysRevD.90.084048

Abstract

On-shell, analytic S-matrix elements in massless theories are constructed from a finite set of primitive three-point amplitudes, which are fixed by Poincare invariance up to an overall numerical constant. We classify \emph{all} such three-point amplitudes in four-dimensions. Imposing the simplest incarnation of Locality and Unitarity on four-particle amplitudes constructed from these three-particle amplitudes rules out all but an extremely small subset of interactions among higher-spin massless states. Notably, the equivalence principle, and the Weinberg-Witten theorem, are simple corollaries of this principle. Further, no massless states with helicity larger than two may consistently interact with massless gravitons. Chromodynamics, electrodynamics, Yukawa and -theories are the only marginal and relevant interactions between massless states. Finally, we show that supersymmetry naturally emerges as a consistency condition on four-particle amplitudes involving spin-3/2 states, which must always interact gravitationally.

33 pages, 2 figures; streamlined abstract and introduction; expanded references to higher-spin literature; modified discussion of the Yukawa-like interaction

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