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Multiple fibrations in Calabi-Yau geometry and string dualities. (English) Zbl 1390.81403
Summary: In this work, we explore the physics associated to Calabi-Yau (CY) \(n\)-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua – associated to different elliptic fibrations of the same CY \(n\)-fold – give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with abelian, non-abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple \(K3\)- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in our companion paper [ibid. 2016, No. 11, Paper No. 4, 58 p. (2016; Zbl 1390.81404)].

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J81 Relationships with physics
14D06 Fibrations, degenerations in algebraic geometry
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J33 Mirror symmetry (algebro-geometric aspects)
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