New Jacobi-like Identities for Zk Parafermion Characters

We state and prove various new identities involving the ZK parafermion characters (or level-K string functions) cn for the cases K = 4, K = 8, and K = 16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi θ-function identity (which is the K = 2 special case), identities in another class relate the level K > 2 characters to the Dedekind η-function, and identities in a third class relate the K > 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.