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Unification of M- and F-theory Calabi-Yau fourfold vacua. (English) Zbl 0973.14509
Summary: 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 non-zero superpotential.

MSC:
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32J18 Compact complex \(n\)-folds
32G81 Applications of deformations of analytic structures to the sciences
32J81 Applications of compact analytic spaces to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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