Level Two String Functions and Rogers Ramanujan Type Identities

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.Comment: 26 page

On the classification of fusion rings

The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion coefficients. We give a catalogue of fusion rings which can arise for these field theories. It is shown that all such fusion rules can be realized by current algebras. Our results support the conjecture that all rational conformal field theories are related to current algebras.Comment: 10 pages, CALT-68-196

Spectral flow as a map between N=(2,0)-models

The space of $(2,0)$ models is of particular interest among all heterotic-string models because it includes the models with the minimal $SO(10)$ unification structure, which is well motivated by the Standard Model of particle physics data. The fermionic $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic-string models revealed the existence of a new symmetry in the space of string configurations under the exchange of spinors and vectors of the $SO(10)$ GUT group, dubbed spinor-vector duality. Such symmetries are important for the understanding of the landscape of string vacua and ultimately for the possible operation of a dynamical vacuum selection mechanism in string theory. In this paper we generalize this idea to arbitrary internal rational Conformal Field Theories (RCFTs). We explain how the spectral flow operator normally acting within a general $(2,2)$ theory can be used as a map between $(2,0)$ models. We describe the details, give an example and propose more simple currents that can be used in a similar way.Comment: 14 pages, v2: minor changes, added one referenc

Field Identifications for Interacting Bosonic Models in N=2 Superconformal Field Theory

We study a family of interacting bosonic representations of the N=2 superconformal algebra. These models can be tensored with a conjugate theory to give the free theory. We explain how to use free fields to study interacting fields and their dimensions, and how we may identify different free fields as representing the same interacting field. We show how a lattice of identifying fields may be built up and how every free field may be reduced to a standard form, thus permitting the resolution of the spectrum. We explain how to build the extended algebra and show that there are a finite number of primary fields for this algebra for any of the models. We illustrate this by studying an example