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×Z2 orbifold of an SO(12) Narain lattice, with (h1,1,h2,1)=(27,3). Alternatively, a manifold with the same data is obtained by starting with a Z2×Z2 orbifold at a generic point on the lattice, with (h1,1,h2,1)=(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.
Highlights
Grand unification, and its incarnation in the form of heterotic-string unification [1], is the only extension of the Standard Model that is rooted in the structure of the Standard Model itself
In this context the most realistic string models discovered to date have been constructed in the heterotic string free fermionic formulation
A large set of realistic free fermionic models contains a subset of boundary conditions, the so-called NAHE set, which can be seen to correspond to Z2 × Z2 orbifold compactification with the standard embedding of the gauge connection [2]
Summary
Its incarnation in the form of heterotic-string unification [1], is the only extension of the Standard Model that is rooted in the structure of the Standard Model itself. The key ingredient in studying the F-theory compactification on the free fermionic Z2 × Z2 orbifold was to connect it to the X1 by a freely acting twist or shift [6]. Part of the geometric moduli are projected out by the orbifold action and, as a result, though the two toroidal models are in the same moduli space, the two Z2 ×Z2 orbifold models are not The connection of these studies to the free fermionic Z2 × Z2 orbifold model rests on the conjecture that the model constructed with the additional freely acting shift is identical to the model at the free fermionic point in the Narain moduli space, i.e. to the Z2 ×Z2 orbifold on the SO(12) lattice. We discuss in this paper the general structure of the partition functions of NAHE based free fermionic models
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