Supersymmetries in Free Fermionic Strings

TL;DR

This paper classifies heterotic free fermionic string models based on their supersymmetry levels, identifying which configurations can produce N=1 supersymmetry and the specific twists compatible with it.

Contribution

It provides a comprehensive classification of supersymmetry in free fermionic string models, determining the conditions and twists that allow N=1 supersymmetry.

Findings

Only three of six gravitino sectors can yield N=1 supersymmetry.

Z_2, Z_4, and Z_8 twists are compatible with N=1.

Most sectors produce N=0, N=2, or N=4 supersymmetry.

Abstract

Consistent heterotic free fermionic string models are classified in terms of their number of spacetime supersymmetries, N. For each of the six distinct choices of gravitino sector, we determine what number of supersymmetries can survive additional GSO projections. We prove by exhaustive search that only three of the six can yield N = 1, in addition to the N = 4, 2, or 0 that five of the six can yield. One choice of gravitino sector can only produce N = 4 or 0. Relatedly, we find that only Z_2, Z_4, and Z_8 twists of the internal fermions with worldsheet supersymmetry are consistent with N=1 in free fermionic models. Any other twists obviate N=1.