Partition functions of NAHE-based free fermionic string models

TL;DR

This paper analyzes the partition functions of NAHE-based free fermionic string models, demonstrating their equivalence to orbifold constructions and exploring how shifts and involutions affect spectra and symmetry breaking.

Contribution

It explicitly constructs the shift reproducing the free fermionic point and shows how related shifts alter the massive spectrum, aiding non-perturbative studies.

Findings

Proven equivalence of NAHE-based models and orbifold constructions.

Explicit realization of shifts reproducing free fermionic compactification.

Different shifts yield the same massless but different massive spectra.

Abstract

The heterotic string free fermionic formulation produced a large class of three generation models, with an underlying SO(10) GUT symmetry which is broken directly at the string level by Wilson lines. A common subset of boundary condition basis vectors in these models is the NAHE set, which corresponds to Z2 X Z2 orbifold of an SO(12) Narain lattice, with (h11,h21)=(27,3). Alternatively, a manifold with the same data is obtained by starting with a Z2 X Z2 orbifold at a generic point on the lattice, with (h11,h21)=(51,3), and adding a freely acting Z2 involution. The equivalence of the two constructions is proven by examining the relevant partition functions. The explicit realization of the shift that reproduces the compactification at the free fermionic point is found. It is shown that other closely related shifts reproduce the same massless spectrum, but different massive spectrum, thus demonstrating the utility of extracting information from the full partition function. A freely acting involution of the type discussed here, enables the use of Wilson lines to break the GUT symmetry and can be utilized in non-perturbative studies of the free fermionic models.