Supersymmetry Breaking and Determination of the Unification Gauge Coupling Constant in String Theories

TL;DR

This paper investigates gaugino condensation in string theories as a mechanism for supersymmetry breaking and gauge coupling determination, finding viable scenarios with hidden matter and multiple condensing groups that yield realistic physical parameters.

Contribution

It provides a systematic, modular invariant analysis showing that multiple hidden condensing groups can naturally produce realistic supersymmetry breaking scales and gauge couplings without fine-tuning.

Findings

Pure Yang-Mills condensation fails to produce realistic gauge couplings.

Presence of hidden matter allows for viable dilaton values and supersymmetry breaking scales.

Results are largely independent of the Green-Schwarz parameter.

Abstract

We study in a systematic and modular invariant way gaugino condensation in the hidden sector as a potential source of hierarchical supersymmetry breaking and a non--trivial potential for the dilaton $S$ whose real part corresponds to the tree level gauge coupling constant (${\rm Re}\ S\sim g_{gut}^{-2}$). For the case of pure Yang--Mills condensation, we show that no realistic results (in particular no reasonable values for ${\rm Re}\ S$) can emerge, even if the hidden gauge group is not simple. However, in the presence of hidden matter (i.e. the most frequent case) there arises a very interesting class of scenarios with two or more hidden condensing groups for which the dilaton dynamically acquires a reasonable value (${\rm Re}\ S\sim 2$) and supersymmetry is broken at the correct scale ($m_{3/2}\sim 10^3\ GeV$) with no need of fine--tuning. Actually, good values for ${\rm Re}\ S$ and $m_{3/2}$ are correlated. We make an exhaustive classification of the working possibilities. Remarkably, the results are basically independent from the value of $\delta^{GS}$ (the contributions from the Green--Schwarz mechanism). The radius of the compactified space also acquires an expectation value, breaking duality spontaneously.