Machine learning of Calabi-Yau volumes

Daniel Krefl, Rak-Kyeong Seong
2017 Physical Review D  
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
more » ... ircumvent 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.
doi:10.1103/physrevd.96.066014 fatcat:4nbbht5jinewlcjdjm3ctx7ea4