New String Theories And Their Generation Number

New heterotic string theories in four dimensions are constructed by tensoring a nonstandard SCFT along with some minimal SCFT's. All such theories are identified and their particle generation number is found. We prove that from the infinite number of new heterotic string theories only the {6} theory predicts three generations as seen in nature which makes it an interesting candidate for further study.Comment: 18 pages, 1 table and no figure

The SO(2r)2\boldsymbol{SO(2r)_2} string functions as q\boldsymbol{q}-diagrams

We discuss our conjecture for simply laced Lie algebras level two string functions of mark one fundamental weights and prove it for the $SO(2r)$ algebra. To prove our conjecture we introduce $q$-diagrams and examine the diagrammatic interpretations of known identities by Euler, Cauchy, Heine, Jacobi and Ramanujan. Interestingly, the diagrammatic approach implies these identities are related in the sense that they represent the first few terms in an infinite series of diagrammatic identities. Furthermore, these diagrammatic identities entail all the identities needed to prove our conjecture as well as generalise it to all $SO(2r)$ level two string functions. As such, our main objective is proving these series of diagrammatic identities thus extending the works mentioned and establishing our conjecture for the $SO(2r)$ level two string functions.Comment: 39 page

The SU(r)2 string functions as q-diagrams

AbstractA generalized Roger Ramanujan (GRR) type expression for the characters of A-type parafermions has been a long standing puzzle dating back to conjectures made regarding some of the characters in the 90s. Not long ago we have put forward such GRR type identities describing any of the level two ADE-type generalized parafermions characters at any rank. These characters are the string functions of simply laced Lie algebras at level two, as such, they are also of mathematical interest. In our last joint paper we presented the complete derivation for the D-type generalized parafermions characters identities. Here we generalize our previous discussion and prove the GRR type expressions for the characters of A-type generalized parafermions. To prove the A-type GRR conjecture we study further the q-diagrams, introduced in our last joint paper, and examine the diagrammatic interpretations of known identities among them Slater identities for the characters of the first minimal model, which is the Ising model, and the Bailey lemma