Quasi-realistic heterotic-string models with vanishing one-loop cosmological constant and perturbatively broken supersymmetry?

TL;DR

This paper presents a string model with broken supersymmetry at one loop, vanishing cosmological constant, and no supersymmetric flat directions, potentially offering a novel approach to stable, realistic string vacua.

Contribution

It introduces a quasi-realistic heterotic-string model with perturbatively broken supersymmetry and zero one-loop cosmological constant, lacking all-order flat directions.

Findings

The model exhibits Bose-Fermi degeneracy leading to zero one-loop cosmological constant.

No all-order solutions for F- and D-flatness are found, suggesting supersymmetry breaking is intrinsic.

Internal moduli are fixed by boundary conditions, potentially stabilizing the vacuum.

Abstract

Quasi-realistic string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopoulos D-term that breaks supersymmetry at the one--loop level in string perturbation theory. Supersymmetry is traditionally restored by imposing F- and D-flatness on the vacuum. By employing the standard analysis of flat directions we present a quasi--realistic three generation string model in which stringent F- and D-flat solution do not appear to exist to all orders in the superpotential. We speculate that this result is indicative of the non-existence of supersymmetric flat F- and D-solutions in this model. We provide some arguments in support of this scenario and discuss its potential implications. Bose-Fermi degeneracy of the string spectrum implies that the one--loop partition function and hence the one-loop cosmological constant vanishes in the model. If our assertion is correct, this model may represent the first known example with vanishing cosmological constant and perturbatively broken supersymmetry. We discuss the distinctive properties of the internal free fermion boundary conditions that may correspond to a large set of models that share these properties. The geometrical moduli in this class of models are fixed due to asymmetric boundary conditions, whereas absence of supersymmetric flat directions would imply that the supersymmetric moduli are fixed as well and the dilaton may be fixed by hidden sector nonperturbative effects.