Advances in Theoretical and Mathematical Physics

Volume 18 (2014)

Number 6

Building blocks for generalized heterotic/F-theory duality

Pages: 1463 – 1503

DOI: http://dx.doi.org/10.4310/ATMP.2014.v18.n6.a7

Authors

Jonathan J. Heckman (Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A.)

Hai Lin (Department of Mathematics and Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A.)

Shing-Tung Yau (Department of Mathematics and Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

In this note we propose a generalization of heterotic/F-theory duality. We introduce a set of non-compact building blocks which we glue together to reach compact examples of generalized duality pairs. The F-theory building blocks consist of non-compact elliptically fibered Calabi-Yau fourfolds which also admit a $K3$ fibration. The compact elliptic model obtained by gluing need not have a globally defined $K3$ fibration. By replacing the $K3$ fiber of each F-theory building block with a $T^2$, we reach building blocks in a heterotic dual vacuum which includes a position dependent dilaton and three-form flux. These building blocks are glued together to reach a heterotic flux background. We argue that in these vacua, the gauge fields of the heterotic string become localized, and remain dynamical even when gravity decouples. This enables a heterotic dual for the hyperflux GUT breaking mechanism which has recently figured prominently in F-theory GUT models. We illustrate our general proposal with some explicit examples.

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