Abstract
We consider heterotic target space dual (0,2) GLSMs on elliptically fibered Calabi-Yau manifolds. In this context, each half of the "dual" heterotic theories must in turn have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple K3-fibrations of the same elliptically fibered Calabi-Yau manifold. In this work we investigate this conjecture in the context of both 6-dimensional and 4-dimensional effective theories and demonstrate that in general, (0,2) target space duality cannot be explained by such a simple phenomenon alone. In all cases, we provide evidence that non-geometric data in F-theory must play at least some role in the induced F-theory correspondence, while leaving the full determination of the putative new F-theory duality to future work.
Highlights
Heterotic target space duality was first observed in [1] and further explored in [2,3,4,5,6]
The apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple K3 fibrations of the same elliptically fibered Calabi-Yau manifold
In an important proof of principle, we have illustrated that heterotic target space duality (TSD) pairs exist in which both halves of the geometry exhibit Calabi-Yau threefolds with elliptic fibrations
Summary
Heterotic target space duality was first observed in [1] and further explored in [2,3,4,5,6]. It could prove that the F-theory duals of heterotic TSD pairs are two distinct CY fourfolds, Y4 and Y 4, whose gauge symmetries, massless spectra, and effective N 1⁄4 1 potentials are the same through nontrivial G-flux in the background geometry We can summarize these two options for the induced duality in F-theory as follows. III, we provide the first nontrivial examples to appear in the literature of heterotic TSD pairs in which both CY threefolds, X and X , are elliptically fibered In these cases, the heterotic geometries are smooth [consisting of smooth so-called complete intersection Calabi-Yau (CICY) threefolds [18] and stable, holomorphic vector bundles defined via the monad construction [19] over them] and lead to well controlled, perturbative heterotic theories. We turn to such an example in which both X and Xare elliptically fibered
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