String theory is a prominent contender for offering a comprehensive explanation of all the physical phenomena we observe. This encompasses a wide spectrum, ranging from the quantum interactions among subatomic particles to the gravitational forces that steer the motion of colossal astronomical objects across galactic expanses. A significant challenge with string theory arises from its immense set of solutions, known as the string landscape. Many of these solutions describe universes with markedly different laws of physics from what we observe in experiments. The pursuit of solutions that align with experimental observations becomes exceedingly demanding, especially as we seek greater consistency between string theory predictions and experimental results. The quest to discover a solution that harmonizes perfectly with all existing experimental observations—while potentially making predictions for future experiments—stands as a revered goal in the realm of string phenomenology. Within this framework, F-theory emerges as a formulation of string theory that manages to encapsulate a substantial portion of the information regarding the various solutions within the string landscape through its geometric aspects. Mathematically, solutions to F-theory correspond to singular elliptically fibered Calabi–Yau manifolds. Given the lack of direct methods of analysis, the F-theory community has adopted the standard approach of first resolving the singularities, and subsequently deriving the underlying physics from the resolved space. The computational process of finding these resolutions is both demanding and occasionally intricate. This chapter illustrates how the application of OSCAR can simplify the computation of resolutions and thereby facilitate the exploration of F-theory solutions.

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F-theory Applications

  • Martin Bies,
  • Andrew P. Turner

摘要

String theory is a prominent contender for offering a comprehensive explanation of all the physical phenomena we observe. This encompasses a wide spectrum, ranging from the quantum interactions among subatomic particles to the gravitational forces that steer the motion of colossal astronomical objects across galactic expanses. A significant challenge with string theory arises from its immense set of solutions, known as the string landscape. Many of these solutions describe universes with markedly different laws of physics from what we observe in experiments. The pursuit of solutions that align with experimental observations becomes exceedingly demanding, especially as we seek greater consistency between string theory predictions and experimental results. The quest to discover a solution that harmonizes perfectly with all existing experimental observations—while potentially making predictions for future experiments—stands as a revered goal in the realm of string phenomenology. Within this framework, F-theory emerges as a formulation of string theory that manages to encapsulate a substantial portion of the information regarding the various solutions within the string landscape through its geometric aspects. Mathematically, solutions to F-theory correspond to singular elliptically fibered Calabi–Yau manifolds. Given the lack of direct methods of analysis, the F-theory community has adopted the standard approach of first resolving the singularities, and subsequently deriving the underlying physics from the resolved space. The computational process of finding these resolutions is both demanding and occasionally intricate. This chapter illustrates how the application of OSCAR can simplify the computation of resolutions and thereby facilitate the exploration of F-theory solutions.