New Jacobi-Like Identities for Z_k Parafermion Characters

TL;DR

This paper introduces new mathematical identities involving Z_K parafermion characters for specific levels, which help interpret fractional superstring spectra and reveal spacetime supersymmetry.

Contribution

It presents novel identities generalizing Jacobi theta-function identities and relating parafermion characters to eta and theta functions for levels 4, 8, and 16.

Findings

Identities generalize Jacobi theta-function identity.

Relations between parafermion characters and Dedekind eta-function.

Connections to spacetime supersymmetry in fractional superstrings.

Abstract

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) 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 theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-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.