Compact, singular G2-holonomy manifolds and M/heterotic/F-theory duality

Abstract

Abstract:We study the duality between M-theory on compact holonomy G 2 -manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G 2 -manifolds, called twisted connected sums, which lend themselves to an application of fiber-wise M-theory/Heterotic Duality. For a large class of such G 2 -manifolds we are able to identify the dual heterotic as well as F-theory realizations. First we establish this chain of dualities for smooth G 2 -manifolds. This has a natural generalization to situations with non-abelian gauge groups, which correspond to singular G 2 -manifolds, where each of the K3-fibers degenerates. We argue for their existence through the chain of dualities, supported by non-trivial checks of the spectra. The corresponding 4d gauge groups can be both Higgsable and non-Higgsable, and we provide several explicit examples of the general construction.

Spin(7)-manifolds as generalized connected sums and 3d $$ \mathcal{N}=1 $$ theories

“…It is known that such Joyce orbifolds have a TCS-decomposition [12], which we apply to the G 2 Joyce orbifold, and subsequently uplift the decomposition to the Spin(7) Joyce orbifold. The TCS-building blocks then map precisely to an open CY 4 and G 2 × S 1 , respectively.…”

“…which is both the Narain moduli space of heterotic string theory on T 3 and the moduli space of Einstein metrics on K3 [37] (for a recent exposition in the context of fiber-wise application see [12]). The string coupling on the heterotic side is matched with the volume modulus of the K3.…”

“…The additional input in this section is that we will consider these in the context of the duality to Heterotic strings theory on G 2 -manifolds, which we show to be TCS-manifolds, with building blocks X ± . Our strategy in finding dual compactifications will be similar to the one we used in [12], i.e. using fiberwise duality between M-theory and heterotic string theory, we will identify dual pairs of building blocks, which can then be glued to find the dual Spin (7) and G 2 -manifolds.…”

“…This is precisely the action required to get the Schoen Calabi-Yau as a Joyce orbifold (see [12] for a detailed discussion of that). Inside X s , there is a K3 surface along z 0 1 , z 0 2 .…”

Marginal deformations of heterotic G2 sigma models

“…Topological twists of the (1, 1) models are also closely related to the generalisation of mirror symmetry to the G 2 setting [39,[63][64][65][66][67]. Since there is a notion of heterotic mirror symmetry in terms of quantum sheaf cohomology, see [68,69] with references therein, one might speculate in analogy that a similar generalisation to the (0, 1) heterotic G 2 setting exists.…”