Generalized String Functions of N=1 Space-Time Supersymmetric String Vacua

TL;DR

This paper develops a dual formulation for N=2 conformal field theories used in string compactifications, revealing their structure through simple currents and string functions, and constructs models with specific gauge symmetries and spectra.

Contribution

It introduces a dual approach to constructing N=2 sigma-model conformal field theories, clarifies their internal structure via simple currents, and provides explicit models with detailed spectra.

Findings

Characterization of supercurrents as tensor products of simple currents

Detailed analysis of string functions in the (1)^9 Gepner model

Construction of a model with 36 E_6 generations and extended gauge symmetry

Abstract

We present a dual formulation of the construction of N=2 nonlinear sigma-model type conformal field theories with c=9 which are mainly used as internal sectors of Calabi-Yau heterotic string compactifications. The supercurrents and the higher components of the spectral flow superfields turn out in each case to be tensor products of two simple currents of a c=1 and a non-supersymmetric parafermionic c=8 CFT. The characters of the latter model can be regarded as string functions of the coset sigma/U(1). In particular, for the (1)^9 Gepner model we discuss these string functions in detail, realizing this model contains a broken E_8 gauge symmetry of which only the abelian subalgebra remains a symmetry of the spectrum. As an example, we construct a simple model leading to a string theory with a massless spectrum of 36 E_6 generations and an extended gauge symmetry E_6 x SU(3)^4.