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Résumé |
Understanding Calabi-Yau metrics and hermitian Yang-Mills connections has long
been a challenge in mathematics and theoretical physics. These geometric objects
play a crucial role in constructing realistic models of particle physics in string
theory. However, with no closed-form expressions for them, we are unable to
compute basic quantities in top-down string models, such as particle masses and
couplings.
Breakthroughs in machine learning have opened a new path to tackle this problem.
After recalling the relationship between these geometric ingredients and 4d
effective field theory, I will review recent progress in using machine learning to
calculate these metrics and connections numerically. Finally, I will highlight how
this newly available geometric data can be used, including studying the spectrum
of Laplace-type operators on a Calabi-Yau in the presence of a background gauge
field. |
