Spinor-vector duality in fermionic [formula omitted] heterotic orbifold models

Abstract

We continue the classification of the fermionic Z 2 × Z 2 heterotic string vacua with symmetric internal shifts. The space of models is spanned by working with a fixed set of boundary condition basis vectors and by varying the sets of independent Generalized GSO (GGSO) projection coefficients (discrete torsion). This includes the Calabi–Yau like compactifications with ( 2 , 2 ) world-sheet superconformal symmetry, as well as more general vacua with only ( 2 , 0 ) superconformal symmetry. In contrast to our earlier classification that utilized a Monte Carlo technique to generate random sets of GGSO phases, in this paper we present the results of a complete classification of the subclass of the models in which the four-dimensional gauge group arises solely from the null sector. In line with the results of the statistical classification we find a bell shaped distribution that peaks at vanishing net number of generations and with ∼15% of the models having three net chiral families. The complete classification reveals a novel spinor-vector duality symmetry over the entire space of vacua. The S t ↔ V duality interchanges the spinor plus anti-spinor representations with vector representations. We present the data that demonstrates the spinor-vector duality. We illustrate the existence of a duality map in a concrete example. We provide a general algebraic proof for the existence of the S t ↔ V duality map. We discuss the case of self-dual solutions with an equal number of vectors and spinors, in the presence and absence of E 6 gauge symmetry, and presents a couple of concrete examples of self-dual models without E 6 symmetry.