Fermion Currents on Asymmetric Orbifolds

TL;DR

This paper investigates the conditions under which fermionic string theory orbifold models can be equivalently expressed as torus models, highlighting the role of asymmetry and lattice automorphisms.

Contribution

It identifies the limitations of symmetric orbifolds in being rewritten as torus models and provides a classification of current algebras for asymmetric $Z_N$-orbifolds with specific lattice automorphisms.

Findings

Symmetric orbifolds cannot be rewritten as torus models due to lack of twist-untwist currents.

Rewriting depends on the choice of momentum lattice and lattice automorphism.

A list of current algebras for asymmetric orbifolds with inner automorphisms is provided.

Abstract

We study whether orbifold models are equivalently rewritten into torus models in the case of fermionic string theories. It is pointed out that symmetric orbifold models cannot be rewritten into torus models in the case of fermionic string theories because of the absence of twist-untwist intertwining currents on the orbifold models. We present a list of current algebras on asymmetric $Z_N$-orbifold models of type II superstring theories with inner automorphisms of Lie algebra lattices of the $A_n$ series. It turns out that whether an asymmetric orbifold model is rewritten into a torus model depends on the specific choice of a momentum lattice and an inner automorphism of the lattice.