Abstract

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 a companion paper [1].

Highlights

  • F-theory has proven to be a flexible and extensive framework for studying the possible effective field theories arising from string compactifications in various dimensions

  • 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

  • From the point of view of F-theory, Weierstrass models correspond to a minimal, irreducible form of the torus fiber that can be directly linked to the axio-dilaton

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Summary

Matter in 6-dimensional F-theory compactifications

We will begin by computing and comparing the massless spectrum of the lower dimensional theories that we consider. At specific codimension-two loci in the base, where selfintersections of the discriminant locus occur, the rank of the non-Abelian singularity of the fiber will enhance. Such enhancements generically lead to matter states and their representations can be obtained from the branching rules from the adjoint representation of the enhanced gauge algebra into the low energy gauge group of the theory [50]. Counting U(1) charged matter that is neutral under the non-Abelian gauge group factors is somewhat more involved Such degrees of freedom are associated with I2 fibers appearing over nodes of the self-intersection of the I1 locus of the discriminant [51]. The computation of this U(1)-charged matter is discussed in detail in appendix A

Anomaly cancelation
Other fibrations with purely Abelian gauge groups
Higher rank Mordell-Weil group
Multiple fibrations and 6-dimensional theories
Multiple fibrations and 4-dimensional theories
Adiabatic 4-dimensional realizations of higher dimensional dualities
Multiple elliptic fibrations in 4-dimensional heterotic compactifications
Exploring the moduli space of stable bundles
A Counting of nodes in a complex curve
A hypersurface curve
A complete intersection curve
B The topology of an elliptically fibered Calabi-Yau 3-fold

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