Effective Mu-Term in Superstring Theory

TL;DR

This paper analyzes the $μ$-term in four-dimensional heterotic string compactifications, showing it can arise after SUSY breaking through three mechanisms: (i) a Kähler potential term quadratic in Higgs fields with moduli-dependent coefficient $H$, (ii) a higher weight F-term producing non-standard interactions that mix with Yukawa couplings, and (iii) explicit non-perturbative superpotential masses from gaugino condensation. In $(2,2)$ orbifolds, both $H$ and its one-loop correction $H^{(1)}$ are expressible in terms of moduli metrics and singlet Yukawas; at tree level untwisted moduli yield $H_{AB} = 1/[(T+ar T)(U+ar U)]$, while twisted moduli can contribute in general. One-loop threshold corrections link to $H^{(1)}$, and gaugino condensation induces direct Higgs masses via moduli-dependent thresholds; the analysis highlights duality constraints and the need to minimize the scalar potential to obtain physical Higgsino masses.

Abstract

In four-dimensional compactifications of the heterotic superstring theory the Kähler potential has a form which generically induces a superpotential mass term for Higgs particles once supersymmetry is broken at low energies. This ``$μ$-term'' is analyzed in a model-independent way at the tree level and in the one-loop approximation, and explicit expressions are obtained for orbifold compactifications. Additional contributions which arise in the case of supersymmetry breaking induced by gaugino condensation are also discussed.