Building blocks for generalized heterotic/F-theory duality. (English) Zbl 1308.81147

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

Adv. Theor. Math. Phys. 18, No. 6, 1463-1503 (2014).

Summary: 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.

MSC:

81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32	Calabi-Yau manifolds (algebro-geometric aspects)
14D06	Fibrations, degenerations in algebraic geometry
81V22	Unified quantum theories
81V17	Gravitational interaction in quantum theory