On-Shell Constraints and the Emergence of Supersymmetry

Recasting QFT in on-shell terms elevates little group covariance, unitarity and analyticity to first principles that constrain allowable dynamics. In the convenient language of spinor-helicity, three-point amplitudes are fixed completely by little group weights, and when considering amplitudes of massless spin 1 particles, one instantly arrives at the need for a Yang-Mills structure, and charge conservation. The analogous analysis on massless spin 2 particles yields the universality and diagonality of gravity. Unitarity, via consistent factorization requirements constraints charged particles to spin less than 3/2 and does not allow gravity to couple to particles of spin greater than 2. Extending this analysis to massless Schwinger-Rarita fields, supersymmetry emerges through the need for factorization, and the super-Yang-Mills and supergravity supermultiplets are uniquely determined. For scalars, the general two-derivative sector, given a soft relation, is uniquely fixed by the Non Linear Sigma Model(NLSM). Factorization and the soft relation fixes the connection to be Levi-Civita, and by induction reconstructs a unique Riemannian metric defining the NLSM. Finally, analyticity and positivity requirements on partial-wave expansions impose bounds on high-energy amplitude behavior, strongly constraining the space of UV-completable low-energy amplitudes. In the case of scalar amplitudes, there is no way to consistently UV complete them with finitely many particles.