the pullback of the Kähler form to the submanifold vanishes. The worldvolume theory on a stack of N D2-branes is the string field theory of the open strings of the A-model, which is a U(N) Chern–Simons theory. The fundamental topological strings may end on the D2-branes. While the embedding of a string depends only on the Kähler form, the embeddings of the branes depends entirely on the complex structure. In particular, when a string ends on a brane the intersection will always be orthogonal, as the wedge product of the Kähler form and the holomorphic 3-form is zero. In the physical string this is necessary for the stability of the configuration, but here it is a property of Lagrangian and holomorphic cycles on a Kahler manifold. There may also be coisotropic branes in various dimensions other than half dimensions of Lagrangian submanifolds. These were first introduced by Anton Kapustin and Dmitri Orlov in Remarks on A-Branes, Mirror Symmetry, and the Fukaya Category B-model The B-model also contains fundamental strings, but their scattering amplitudes depend entirely upon the complex structure and are independent of the Kähler structure. In particular, they are insensitive to worldsheet instanton effects and so can often be calculated exactly. Mirror symmetry then relates them to A model amplitudes, allowing one to compute Gromov–Witten invariants. The string field theory of the closed strings of the B-model is known as the Kodaira–Spencer theory of gravity and was developed by Michael Bershadsky, Sergio Cecotti, Hirosi Ooguri and Cumrun Vafa in Kodaira–Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes. The B-model also comes with D(-1), D1, D3 and D5-branes, which wrap holomorphic 0, 2, 4 and 6-submanifolds respectively. The 6-submanifold is a connected component of the spacetime. The theory on a D5-brane is known as holomorphic Chern–Simons theory. The Lagrangian density is the wedge product of that of ordinary Chern–Simons theory with the holomorphic (3,0)-form, which exists in the Calabi–Yau case. The Lagrangian densities of the theories on the lower-dimensional branes may be obtained from holomorphic Chern–Simons theory by dimensional reductions. Topological M-theory Topological M-theory, which enjoys a seven-dimensional spacetime, is not a topological string theory, as it contains no topological strings. However topological M-theory on a circle bundle over a 6-manifold has been conjectured to be equivalent to the topological A-model on that 6-manifold. In particular, the D2-branes of the A-model lift to points at which the