Heterotic parafermionic superstring

Superstrings have been postulated based on parafermionic partition functions which permit spacetime supersymmetry by generalized Jacobi identities. A comprehensive search finds new such identities. Quadrilateral anomaly cancellation gives constraints on allowed chiral fermions. Bosonic left movers and ${\mathit{Z}}_4$ parafermionic right movers combine in a new heterotic superstring, more constrained than the old one, yet equally applicable to physics.