Machine learning on generalized complete intersection Calabi-Yau manifolds

Generalized Calabi-Yau manifolds

A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2-forms. In the special case of six dimensions we characterize them as critical points of a natural variational problem on clos...

Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kähler form e and the holomorphic form Ω. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Mor...

Calabi-Yau Manifolds

Rigid curves in complete intersection Calabi-Yau threefolds

Working over the complex numbers, we study curves lying in a complete intersection K3 surface contained in a (nodal) complete intersection Calabi-Yau threefold. Under certain generality assumptions, we show that the linear system of curves in the surface is a connected componend of the the Hilbert scheme of the threefold. In the case of genus one, we deduce the existence of infinitesimally rigi...

Machine learning of Calabi-Yau volumes

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 n...