The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case

Understand

Four-form flux in F-theory compactifications not only stabilizes moduli, but gives rise to ensembles of string vacua, providing a scientific basis for a stringy notion of naturalness.

• Of particular interest in this context is the ability to keep track of algebraic information (such as the gauge group) associated with individual vacua while dealing with statistics.
• In the present work, we aim to clarify conceptual issues and sharpen methods for this purpose, using compactification on ${\rm K3} \times {\rm K3}$ as a test case.
• Our first approach exploits the connection between the stabilization of complex structure moduli and the Noether-Lefschetz problem.