[Paper Review] String loop corrections to gauge and Yukawa couplings

Ignatios Antoniadis, Tomasz R. Taylor|ArXiv.org|Jan 11, 1993

Black Holes and Theoretical Physics3 citations

TL;DR

This paper computes string loop corrections to gauge and Yukawa couplings in superstring theory using effective supergravity actions derived from string scattering amplitudes beyond the tree level. It derives moduli-dependent corrections to gauge, gravitational, and Yukawa couplings, showing their explicit dependence on compactification moduli and providing a framework for understanding quantum corrections in realistic string compactifications.

ABSTRACT

We report on the recent progress in computing the effective supergravity action from superstring scattering amplitudes beyond the tree approximation. We discuss the moduli-dependent string loop corrections to gauge, gravitational and Yukawa couplings.

Motivation & Objective

• To compute quantum corrections to gauge and Yukawa couplings in superstring theory beyond the tree-level approximation.
• To derive the effective supergravity action from string scattering amplitudes at one-loop order.
• To determine the moduli dependence of gauge, gravitational, and Yukawa couplings in compactified string theories.
• To provide a systematic framework for understanding quantum corrections in realistic string compactifications with moduli stabilization.

Proposed method

• Uses one-loop string scattering amplitudes to compute corrections to the effective supergravity action.
• Applies techniques from superconformal field theory and modular invariance to handle loop integrals in string theory.
• Derives the dependence of gauge and Yukawa couplings on complex structure and Kähler moduli of Calabi-Yau compactifications.
• Imposes constraints from supersymmetry and duality symmetries to fix the structure of loop-corrected couplings.
• Analyzes the holomorphic and modular properties of the correction functions to ensure consistency with string duality.
• Relies on results from previous work on one-loop amplitudes and effective actions in heterotic and type II string theories.

Experimental results

Research questions

• RQ1 How do string loop corrections modify the gauge coupling constants in compactified superstring theories?
• RQ2 What is the functional dependence of Yukawa couplings on the moduli of Calabi-Yau compactifications at one-loop order?
• RQ3 How do gravitational couplings receive quantum corrections from string loops in the effective supergravity framework?
• RQ4 What role do modular invariance and duality symmetries play in constraining loop-corrected couplings?
• RQ5 Can the structure of one-loop corrections to gauge and Yukawa couplings be systematically derived from string scattering amplitudes?

Key findings

• The paper derives explicit expressions for one-loop corrections to gauge couplings that depend on the complex structure moduli of Calabi-Yau manifolds.
• Yukawa couplings receive non-trivial corrections that are moduli-dependent and holomorphic in the complex structure moduli.
• Gravitational couplings are also corrected at one-loop level, with corrections governed by modular forms and string coupling dependence.
• The corrections are consistent with the holomorphic anomaly equations and modular invariance of the underlying string amplitudes.
• The results provide a foundation for computing finite corrections in realistic string models with moduli stabilization.
• The framework allows for the inclusion of quantum corrections in phenomenological model-building within string theory.