Abstract
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 G2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M4] on the other.
Highlights
L (X7, M4) of a G2 holonomy manifold X7 and a coassociative submanifold M4 in it
While the study of borderedholomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves 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 G2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T 2 fibrations
Summary
If one wants to construct the simplest model labeled by (X, S, L), for the choice of X nothing can be simpler than C3. Once we introduced the key players, X, S, and L, they appear to define a perfectly sensible configuration of NS5 and D4-branes (1.7) with world-volumes R2 × S and R2 × L, respectively. This choice of (X, S, L), suffers from an important anomaly. As it stands, the triple (X, S, L) introduced here does not define a consistent model and, in particular, does not admit a lift (1.1) to a coassociative submanifold M4 ⊂ X7 or to a Spin(7) manifold X8
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