New Jacobi-like identities for Z K parafermion characters

Abstract

We state and prove various new identities involving theZ K parafermion characters (or level-K string functions)c l n for the casesK=4,K=8, andK=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi ϑ-function identity (which is theK=2 special case), identities in another class relate the levelK>2 characters to the Dedekind η-function, and identities in a third class relate theK>2 characters to the Jacobi ϑ-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.