Abstract
We employ machine learning techniques to investigate the volume minimum of Sasaki-Einstein base manifolds of non-compact toric Calabi-Yau 3-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 3-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.
Highlights
In recent years, machine learning has become a cornerstone for many fields of science, and it has been adopted more and more as a valuable toolbox
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
Using a large data set of toric Calabi-Yau three-folds, our aim is to train a machine learning model in such a way that it approximates a functional relationship between topological quantities of the toric Calabi-Yau three-fold and the minimum volume of the Sasaki-Einstein base manifold
Summary
Machine learning has become a cornerstone for many fields of science, and it has been adopted more and more as a valuable toolbox. Using a large data set of toric Calabi-Yau three-folds, our aim is to train a machine learning model in such a way that it approximates a functional relationship between topological quantities of the toric Calabi-Yau three-fold and the minimum volume of the Sasaki-Einstein base manifold. Such a functional relation would be of great use because it would circumvent the standard volume minimization procedure and highlight a direct relationship between topological quantities of the toric Calabi-Yau geometries and the central charges of the 4d superconformal field theories. We refer the reader to [10] for a basic introduction on CNN models and [11] for a comprehensive reference list
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