An N=1 Triality by Spectrum Matching

TL;DR

This paper explores a triality connecting heterotic, M-theory, and F-theory compactifications via spectrum matching on specific manifolds, revealing new dualities and puzzles in string theory geometry.

Contribution

It proposes a novel triality among heterotic, M-theory, and F-theory compactifications using spectrum matching on barely G_2 manifolds and Calabi-Yau constructions, highlighting unexpected geometric properties.

Findings

Identifies a triality between heterotic, M-theory, and F-theory compactifications.

Discovers a puzzle regarding the Hodge data of certain Calabi-Yau 4-folds.

Studies properties of antiholomorphic involutions in manifold constructions.

Abstract

On promoting the type IIA side of the N=1 Heterotic/type IIA dual pairs of [1] to M-theory on a `barely G_2 Manifold' of [2], by spectrum-matching we show a possible triality between Heterotic on a self-mirror Calabi-Yau, M-theory on the above `barely G_2-Manifold' constructed from the Calabi-Yau on the type IIA side and $F$-theory on an elliptically fibered Calabi-Yau 4-fold fibered over a trivially rationally ruled CP^1 x E base, E being the Enriques surface. We raise an apparent puzzle on the F-theory side, namely, the Hodge data of the 4-fold derived can not be obtained by a naive freely acting orbifold of CY_3(3,243) x T^2 as one might have guessed on the basis of arguments related to dualities involving string, M and (definition of) F theories. There are some interesting properties of the antiholomorphic involution used in \cite{VW} for constructing the type IIA orientifold and by us in constructing the 'barely G_2 manifold', that we also study.