[Paper Review] Theoretical and Phenomenological Aspects of Superstring Theories

Christos Kokorelis|arXiv (Cornell University)|Dec 7, 1998

Black Holes and Theoretical Physics36 references3 citations

TL;DR

This PhD thesis investigates threshold corrections and prepotential calculations in heterotic string compactifications using orbifold constructions, focusing on (2,2) and (0,2) non-decomposable models. It derives moduli-dependent gauge couplings via generalized Coxeter automorphisms and identifies Hauptmoduln for congruence subgroups, providing evidence for the stringy Higgs effect and linking to μ-term generation and gaugino condensation in effective field theories.

ABSTRACT

We discuss aspects of the heterotic string effective field theories in orbifold constructions of the heterotic string. We calculate the moduli dependence of threshold corrections to gauge couplings in (2,2) symmetric orbifold compactifications. We perform the calculation of the threshold corrections for a particular class of abelian (2,2) symmetric non-decomposable orbifold models... internal twist is realized as generalized Coxeter automorphism. We define the limits for the existence of states causing singularities in the moduli space in the perturbative regime for a generic vacuum of the heterotic string. The 'proof' provides evidence for the explanation of the stringy 'Higgs effect'. Furthermore, we calculate the moduli dependence of threshold corrections as target space invariant free energies for non-decomposable orbifolds, identifying the Hauptmodul' functions for the relevant congruence subgroups. The required solutions provide for the μmass term generation in the effective low energy theory and affect the induced sypersymmetry breaking by gaugino condensation. In addition, we discuss the one loop gauge and gravitational couplings in (0,2) non-decomposable orbifold compactifications. In the second part of the Thesis the one loop correction to the Kahler metric for a generic N=2 orbifold compactification of the heterotic string is calculated... In this way, with the use of the one loop string amplitudes, the prepotential of the vector multiplets of the N=2 effective low-energy heterotic string is calculated in decomposable toroidal compactifications of the heterotic string ... This method provides the solution for the one loop correction to the prepotential of the vector multiplets of the heterotic string compactified on the K_3 imes T^2...

Motivation & Objective

• To understand the moduli dependence of gauge coupling threshold corrections in (2,2) symmetric orbifold compactifications of the heterotic string.
• To analyze the existence conditions for singular states in moduli space within perturbative heterotic vacua.
• To calculate one-loop corrections to the Kähler metric and prepotential in N=2 orbifold compactifications.
• To identify the role of Hauptmoduln functions in non-decomposable orbifold models and their implications for low-energy effective theories.
• To connect string amplitudes to the generation of the μ term and supersymmetry breaking via gaugino condensation.

Proposed method

• Uses one-loop string amplitudes to compute the prepotential of vector multiplets in decomposable toroidal compactifications.
• Applies generalized Coxeter automorphisms to realize internal twists in (2,2) non-decomposable orbifold models.
• Calculates threshold corrections as target-space-invariant free energies, identifying relevant congruence subgroups.
• Derives the moduli dependence of gauge couplings through explicit computation in symmetric orbifold constructions.
• Relies on modular invariance and automorphic forms to determine the structure of the effective field theory.
• Connects the resulting prepotential and threshold corrections to phenomenological features such as the μ term and gaugino condensation.

Experimental results

Research questions

• RQ1 How do threshold corrections to gauge couplings depend on moduli in (2,2) symmetric orbifold compactifications of the heterotic string?
• RQ2 What are the conditions under which singular states appear in the moduli space of heterotic string vacua in the perturbative regime?
• RQ3 Which Hauptmoduln functions arise from the free energy calculations in non-decomposable (2,2) orbifold models, and what congruence subgroups do they correspond to?
• RQ4 How do one-loop corrections to the Kähler metric and prepotential emerge in N=2 orbifold compactifications of the heterotic string?
• RQ5 What is the connection between the derived prepotential and the generation of the μ term and supersymmetry breaking via gaugino condensation?

Key findings

• The moduli dependence of threshold corrections is computed explicitly for a class of abelian (2,2) symmetric non-decomposable orbifold models using generalized Coxeter automorphisms.
• The existence of singular states in moduli space is constrained by derived limits, supporting the stringy Higgs effect in perturbative vacua.
• The threshold corrections are expressed as target-space-invariant free energies, and the relevant Hauptmoduln functions are identified for specific congruence subgroups.
• The one-loop correction to the prepotential of vector multiplets is derived for K_3 × T^2 compactifications via string amplitude techniques.
• The prepotential calculation provides a framework for understanding μ-term generation and induced supersymmetry breaking through gaugino condensation.
• One-loop gauge and gravitational couplings are computed in (0,2) non-decomposable orbifold compactifications, extending the phenomenological reach of the model.