Abstract
We describe a class of compact G2 orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective superpotential of M-theory compactifications. Under a chain of dualities, these can be mapped to F-theory on a Calabi-Yau fourfold, and we find that they are dual to an example studied by Donagi, Grassi and Witten. Finally, we give two different descriptions of our main example and the associative submanifolds as a twisted connected sum.
Highlights
It is relatively straightforward to find the classical superpotential in supergravity, the full theory receives non-perturbative corrections, which can typically be understood as arising from instantonic branes
We describe a class of compact G2 orbifolds constructed from non-symplectic involutions of K3 surfaces
We identify a model for which there are infinitely many associative submanifolds contributing to the effective superpotential of M theory compactifications
Summary
A 7-manifold M 7 whose holonomy group is the exceptional group G2 may be characterised by the existence of a G2-invariant 3-form φ. In most of Joyce’s examples, the starting manifold is either a flat 7-torus T 7 or X × T 3, with X a hyper-Kahler K3 surface and the quotients are chosen so that the singularities may be removed by gluing in model metrics with either SU(2) or SU(3) holonomy. Given the form of φ above, a natural class of associatives in M arise either from holomorphic curves Σ ⊂ X or special Lagrangian surfaces in X The former are calibrated by the Kahler form, the latter by the real part of a holomorphic volume form. This setting allows for the construction of examples with infinitely many, homologically distinct associative 3-spheres in certain G2-orbifolds
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
