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Machine learning of Calabi-Yau volumes
CERN, Theoret Phys Dept, CH-1211 Geneva 23, Switzerland..
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2017 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 96, no 6, article id 066014Article in journal (Refereed) Published
Abstract [en]

We employ machine learning techniques to investigate the volume minimum of Sasaki-Einstein base manifolds of noncompact toric Calabi-Yau three-folds. We find that the minimum volume can be approximated via a second-order multiple linear regression on standard topological quantities obtained from the corresponding toric diagram. The approximation improves further after invoking a convolutional neural network with the full toric diagram of the Calabi-Yau three-folds as the input. We are thereby able to circumvent any minimization procedure that was previously necessary and find an explicit mapping between the minimum volume and the topological quantities of the toric diagram. Under the AdS/CFT correspondence, the minimum volumes of Sasaki-Einstein manifolds correspond to central charges of a class of 4d N = 1 superconformal field theories. We therefore find empirical evidence for a function that gives values of central charges without the usual extremization procedure.

Place, publisher, year, edition, pages
American Physical Society, 2017. Vol. 96, no 6, article id 066014
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:uu:diva-336484DOI: 10.1103/PhysRevD.96.066014ISI: 000410456800013OAI: oai:DiVA.org:uu-336484DiVA, id: diva2:1166314
Available from: 2017-12-14 Created: 2017-12-14 Last updated: 2017-12-14Bibliographically approved

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Seong, Rak-Kyeong
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