cymyc: C alabi- Y au M etrics, Y ukawas, and C urvature
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We introduce cymyc, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. cymyc includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.
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Acknowledgements: The authors would like to thank Oisin Kim, Theodore Long, and Daniel Platt for helpful discourse. JT would like to thank the organisers of the ‘Machine learning in infinite dimensions’ workshop in Bath, August 2024, where most of the work on this paper was undertaken. PB and GB are supported in part by the Department of Energy grant DE-SC0020220. TH is grateful to the Department of Mathematics, University of Maryland, College Park, and the Physics Department of the Faculty of Natural Sciences of the University of Novi Sad, Serbia, for the recurring hospitality and resources. VJ is supported by the South African Research Chairs Initiative of the Department of Science and Innovation and the National Research Foundation. DM is supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020. DM would also like to thank the Abdus Salam ICTP for hospitality and scientific exchange during the Workshop and School on Number Theory and Physics in June 2024. CM is supported by a fellowship with the Accelerate Science program at the Computer Laboratory, University of Cambridge. JT is supported by a studentship with the Accelerate Science Program.
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