# Machine Learning of Calabi-Yau Volumes

## TL;DR

This paper uses machine learning to predict the minimum volume of Sasaki-Einstein manifolds from topological data, enabling direct estimation of central charges in related superconformal field theories without complex minimization.

## Contribution

It introduces a novel machine learning approach, combining linear regression and neural networks, to directly map topological quantities to minimum volumes of Calabi-Yau manifolds.

## Key findings

- Second order linear regression approximates minimum volume.
- Neural networks improve approximation accuracy.
- Explicit mapping between topological data and volume established.

## 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.