Untwisted Moduli and Internal Fermions in Free Fermionic Strings

TL;DR

This paper analyzes how boundary conditions in free fermionic string models influence the number and type of untwisted moduli, providing a geometric interpretation and proving the results through world-sheet supersymmetry considerations.

Contribution

It offers a comprehensive analysis of boundary condition effects on moduli in free fermionic strings, including a geometric description and general proof via world-sheet supersymmetry.

Findings

Number of moduli depends on internal fermions and boundary conditions.

Type of moduli determined by world-sheet left-right asymmetry.

World-sheet supersymmetry constrains boundary conditions.

Abstract

We investigate the dependence of the number and type of untwisted moduli on the boundary condition vectors of relistic free fermionic strings. The number of moduli is given by six minus the number of complex internal world--sheet fermions and the type of moduli is determined by the details of the world--sheet left--right asymmetry of the boundary conditions for the internal fermions. We give a geometrical description of our results in terms of the transformations of the compactified dimensions of $Z_2 \times Z_2$ orbifolds. We investigate all possible boundary conditions for the internal fermions and prove our results in general by showing that world--sheet supersymmetry eliminates those boundary conditions which violate our results.