Asymmetric Gepner Models III. B-L Lifting

TL;DR

This paper introduces B-L lifting, a method to replace the U(1)_{B-L} symmetry in heterotic string models with alternative structures, enabling the construction of chiral spectra in Gepner models.

Contribution

It extends heterotic weight lifting techniques to Gepner models by applying B-L lifting, identifying conditions for chiral spectra and analyzing numerous invariants.

Findings

86 Gepner model invariants have the required order 5 simple current

69 invariants produce chiral spectra

Three-family spectra are common

Abstract

In the same spirit as heterotic weight lifting, B-L lifting is a way of replacing the superfluous and ubiquitous U(1)_{B-L} with something else with the same modular properties, but different conformal weights and ground state dimensions. This method works in principle for all variants of (2,2) constructions, such as orbifolds, Calabi-Yau manifolds, free bosons and fermions and Gepner models, since it only modifies the universal SO(10) x E_8 part of the CFT. However, it can only yield chiral spectra if the ``internal" sector of the theory provides a simple current of order 5. Here we apply this new method to Gepner models. Including exceptional invariants, 86 of them have the required order 5 simple current, and 69 of these yield chiral spectra. Three family spectra occur abundantly.