Advances in Theoretical and Mathematical Physics

Building blocks for generalized heterotic/F-theory duality

Jonathan J. Heckman, Hai Lin, and Shing-Tung Yau

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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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Adv. Theor. Math. Phys., Volume 18, Number 6 (2014), 1463-1503.

First available in Project Euclid: 4 December 2014

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Heckman, Jonathan J.; Lin, Hai; Yau, Shing-Tung. Building blocks for generalized heterotic/F-theory duality. Adv. Theor. Math. Phys. 18 (2014), no. 6, 1463--1503.

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