Quantum anomalies from three-point on-shell bootstrap

Abstract

We bootstrap quantum anomalies using on-shell techniques in the simplest setting: at three points. The necessary field-theoretic input includes the local or global classical symmetry, which the anomaly may break, and the symmetries of the effective action --- though not its explicit form. We use massless helicity spinors together with an on-shell representation of the discrete C, P, and T transformations. Our approach determines the Weyl, chiral (global and local), diffeomorphism, and Lorentz anomalies up to real constant prefactors and terms that vanish on shell. In particular, we recover gauge-anomaly cancellation conditions, as well as find that the Weyl anomaly should not involve Pontryagin densities.

9 pages + appendices + refs, 2 tables; v2 small improvements throughout, clarified covariant vs consistent anomalies, appendices & refs added