Unification of M- and F- Theory Calabi-Yau Fourfold Vacua

TL;DR

This paper explores splitting type phase transitions between Calabi-Yau fourfolds, revealing connections between different vacua in M- and F-theory, and extending the landscape of known geometries.

Contribution

It introduces a generalized framework for phase transitions between Calabi-Yau fourfolds, unifying M- and F-theory vacua and expanding the class of known geometries.

Findings

Connected vacua with zero and nonzero superpotential.

Extended the class of Calabi-Yau fourfolds to include weighted configurations.

Demonstrated transitions between different moduli space dimensions.

Abstract

We consider splitting type phase transitions between Calabi-Yau fourfolds. These transitions generalize previously known types of conifold transitions between threefolds. Similar to conifold configurations the singular varieties mediating the transitions between fourfolds connect moduli spaces of different dimensions, describing ground states in M- and F-theory with different numbers of massless modes as well as different numbers of cycles to wrap various p-branes around. The web of Calabi-Yau fourfolds obtained in this way contains the class of all complete intersection manifolds embedded in products of ordinary projective spaces, but extends also to weighted configurations. It follows from this that for some of the fourfold transitions vacua with vanishing superpotential are connected to ground states with nonzero superpotential.