AN $\mathcal{N}=1$ TRIALITY BY SPECTRUM MATCHING

Abstract

On promoting the type IIA side of the [Formula: see text] heterotic/type IIA dual pairs of Ref. 1 to M-theory on a "barely G2 manifold" of Ref. 2, by spectrum-matching we show a possible triality between heterotic, M and F theories. The manifolds that figure in this triality are a self-mirror Calabi–Yau, a barely G2 manifold and an elliptically fibered Calabi–Yau four-fold with trivially rationally ruled CP1× Enriques surface base, respectively. We raise an apparent puzzle on the F-theory side, namely, the Hodge data of the 4-fold derived cannot be obtained by a naive freely acting orbifold of CY 3(3,243)×T2 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 Ref. 1 for constructing the type IIA orientifold and by us in constructing the "barely G2 manifold," that we also study.