Gauge and Matter Condensates in Realistic String Models

TL;DR

This paper investigates how gauge and matter condensates in free fermionic string models influence observable physics, highlighting the role of superpotential terms and modular invariance, with explicit calculations in a flipped SU(5) model.

Contribution

It reveals the impact of superpotential structure and modular invariance on vacuum degeneracy and condensate calculations in realistic string models.

Findings

Degenerate vacua can be lifted by higher order superpotential terms.

Explicit computation of gaugino and matter condensates in a flipped SU(5) model.

Modular invariance constrains condensate values and vacuum structure.

Abstract

We examine the inter-relationship of the superpotential containing hidden and observable matter fields and the ensuing condensates in free fermionic string models. These gauge and matter condensates of the strongly interacting hidden gauge groups play a crucial role in the determination of the physical parameters of the observable sector. Supplementing the above information with the requirement of modular invariance, we find that a generic model with only trilinear superpotential allows for a degenerate (and sometimes pathological) set of vacua. This degeneracy may be lifted by higher order terms in the superpotential. We also point out some other subtle points that may arise in calculations of this nature. We exemplify our observations by computing explicitly the modular invariant gaugino and matter condensates in the flipped SU(5) string model with hidden gauge group $SO(10)\times SU(4)$.