[Paper Review] Effective Mu-Term in Superstring Theory

Ignatios Antoniadis, E. Gava+2 more|OpenGrey (Institut de l'Information Scientifique et Technique)|May 4, 1994

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates the generation of an effective μ-term in four-dimensional compactifications of heterotic superstring theory, showing that the Kähler potential naturally induces a superpotential mass term for Higgs fields when supersymmetry is broken at low energies. Using tree-level and one-loop calculations in orbifold compactifications, the authors derive explicit expressions for the μ-term and analyze additional contributions from gaugino condensation, resolving inconsistencies at special moduli points.

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.

Motivation & Objective

• To understand the origin of the μ-term in four-dimensional heterotic superstring compactifications where supersymmetry is broken at low energies.
• To analyze the μ-term in a model-independent way at tree level and in one-loop approximation.
• To derive explicit expressions for the μ-term in orbifold compactifications of the heterotic string.
• To examine additional μ-term contributions arising from supersymmetry breaking via gaugino condensation.
• To resolve inconsistencies in the μ-term at special moduli space points where extra massless states appear.

Proposed method

• Analyzes the Kähler potential in four-dimensional compactifications of the heterotic superstring to derive the effective μ-term.
• Applies tree-level and one-loop calculations to compute the μ-term in orbifold models.
• Uses explicit compactification on Z_N and Z_2×Z_2 orbifolds to obtain quantitative expressions.
• Incorporates effects of gaugino condensation in the one-loop computation of the μ-term.
• Considers moduli space dependence and resolves singularities due to extra massless states at special points.
• Employs standard supergravity techniques and superstring vacuum amplitude methods to compute the effective superpotential.

Experimental results

Research questions

• RQ1 How does the Kähler potential in heterotic string compactifications generate an effective μ-term for Higgs fields upon supersymmetry breaking?
• RQ2 What are the explicit one-loop contributions to the μ-term in orbifold compactifications of the heterotic string?
• RQ3 How do gaugino condensation effects modify the μ-term in low-energy effective field theories?
• RQ4 What happens to the μ-term at special points in the moduli space where additional massless states appear?
• RQ5 Can a consistent and finite μ-term be derived in string-theoretic models with broken supersymmetry?

Key findings

• The μ-term arises naturally from the Kähler potential in four-dimensional heterotic compactifications when supersymmetry is broken at low energies.
• Explicit one-loop expressions for the μ-term are derived in Z_N and Z_2×Z_2 orbifold compactifications.
• Additional μ-term contributions emerge from gaugino condensation, modifying the tree-level result.
• At special moduli points with enhanced gauge symmetry, extra massless states lead to singularities in the μ-term, which are resolved in the revised version.
• The final expressions for the μ-term are finite and well-defined, even at these singular points, due to proper treatment of the vacuum amplitude and moduli dependence.