Speaker
Description
We show that anomaly cancellation, usually imposed as a condition for quantum consistency, can also serve as a principle for organizing particle spectra in chiral gauge theories. For a broad class of spectra charged under both a vector-like gauge symmetry and a chiral gauge symmetry, the anomaly equations are exactly equivalent to the degree-3 Prouhet–Tarry–Escott problem in number theory. This correspondence turns charge consistency into a classification principle for particle spectra. In a minimal realization involving light minicharged particles, it implies a robust lower bound of four mass eigenstates and identifies paired states with the same minicharge and nearby masses. These spectra provide concrete targets for laboratory, astrophysical, and cosmological searches, while assigning physical significance to distinguished Prouhet–Tarry–Escott solutions. Our results show that quantum consistency can determine observable features of hidden charged matter, linking anomaly cancellation, number theory, and particle phenomenology.