On the Characters of Parafermionic Field Theories

Abstract

We study cosets of the type H l /U (1) r , where H is any Lie algebra at level l and rank r. These theories are parafermionic and their characters are related to the string functions, which are generating functions for the multiplicities of weights in the affine representations. An identity for the characters is described, which apply to all the algebras and all the levels. The expression is of the Rogers Ramanujan type. We verify this conjecture, for many algebras and levels, using Freudenthal Kac formula, which calculates the multiplicities in the affine representations, recursively, up to some grade. Our conjecture encapsulates all the known results about these string functions, along with giving a vast wealth of new ones.

Generalized Rogers–Ramanujan identities for twisted affine algebras

“…In ref. [12] we found many such generalizations for the untwisted algebras. Unfortunately, the naive guess does not work for the twisted algebras, but we are confident that with more work, such GRR expressions could be found.…”

“…In the work [12] we presented GRR identities which express the characters of generalized parafermions [13].…”

“…We wish to generalize the Slater identities to parafermionic field theories which are generalizations of the Ising model. In the work [12] we presented GRR identities which express the characters of generalized parafermions [13].…”

Generalized Rogers Ramanujan Expressions for Some Non--Singlet Twisted Affine Algebras

“…In a seminal work, Lepowsky and Primc found such expressions for SU (2) [4]. Later, GRR expressions for the untwisted affine algebras were given for the singlet representation [5], and generalized to some other representations in [6]. These GRR expressions, for the untwisted algebras, were recently proved in [7].…”