Quadrillion F-Theory Compactifications with the Exact Chiral Spectrum of the Standard Model

Area of Science:

• High Energy Physics
• String Theory
• Algebraic Geometry

Background:

• String theory compactifications aim to reconcile particle physics with quantum gravity.
• F-theory provides a framework for studying string compactifications.
• Achieving the Standard Model's chiral spectrum is a key challenge.

Purpose of the Study:

• To explore a vast landscape of F-theory compactifications.
• To find models with the exact chiral spectrum of the Standard Model.
• To investigate automatic gauge coupling unification in these models.

Main Methods:

• Utilizing F-theory on elliptically fibered Calabi-Yau fourfolds.
• Applying algebraic geometry to analyze global consistency conditions.
• Focusing on toric bases and associated polytopes.

Main Results:

• Discovered over 10^15 globally consistent F-theory compactifications.
• These compactifications yield the exact chiral spectrum of the Standard Model.
• Gauge coupling unification is automatically realized.

Conclusions:

• A large number of F-theory models can realize the Standard Model.
• The framework naturally incorporates gauge coupling unification.
• This work provides a rich landscape for model building in particle physics.