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.

arXiv comment13 pages. The fortran program ALGEBRA.for is available from the source files

References in corpus (8)

• Fermionic Sum Representations for Conformal Field Theory Characters
• Fermionic Character Sums and the Corner Transfer Matrix
• Quasi-Particles, Conformal Field Theory, and $q$-Series
• Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz
• Generalized Rogers Ramanujan Identities from AGT Correspondence
• Lattice models and generalized Rogers Ramanujan identities
• Fermionic Sum Representations for the Virasoro Characters of the Unitary Superconformal Minimal Models
• Level Two String Functions and Rogers Ramanujan Type Identities

Cited by in corpus (4)

• Parafermionic bases of standard modules for affine Lie algebras
• The $\mathbf{SO}(2\mathbf{r}{)}_2$ string functions as $\mathbf{q}$-diagrams
• Generalized Rogers Ramanujan Identities for Twisted Affine Algebras
• Generalized Rogers Ramanujan Expressions for Some Non--Singlet Twisted Affine Algebras