"Lagrangian Disks" in M-theory

While the study of bordered (pseudo-)holomorphic curves with boundary on
Lagrangian submanifolds has a long history, a similar problem that involves
(special) Lagrangian submanifolds with boundary on complex surfaces appears to
be largely overlooked in both physics and math literature. We relate this
problem to geometry of coassociative submanifolds in $G_2$ holonomy spaces and
to $Spin(7)$ metrics on 8-manifolds with $T^2$ fibrations. As an application to
physics, we propose a large class of brane models in type IIA string theory
that generalize brane…