PUPT 2454 Higher-spin massless S-matrices in four-dimensions

On-shell, analytic S-matrix elements in massless theories are constructed from a fi-nite set of primitive three-point amplitudes, which are fixed by Poincare invariance up to an overall numerical constant. We classify 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. Fur-ther, no massless states with helicity larger than two may consistently interact with massless gravitons. Chromodynamics, electrodynamics, Yukawa and φ3-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. ar X i