Level Two String Functions and Rogers Ramanujan Type Identities

Abstract

The level two string functions are calculated exactly for all simply laced Lie algebras, using a ladder coset construction. These are the characters of cosets of the type $G/U(1{)}^r$, where $G$ is the algebra at level two and $r$ is its rank. This coset is a theory of generalized parafermions. A conjectured Rogers Ramanujan type identity is described for these characters. Using the exact string functions, we verify the Rogers Ramanujan type expressions, that are the main focus of this work.

26 pages

References in corpus (7)

• 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

Cited by in corpus (4)

• On The Characters of Parafermionic Field Theories
• 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