has no dynamics. Instead, all observables depend on the topology of a configuration. Such theories are known as topological theories. Classically this procedure is always possible. Quantum mechanically, the U(1) symmetries may be anomalous, making the twist impossible. For example, in the Kähler case with H = 0 the twist leading to the A-model is always possible but that leading to the B-model is only possible when the first Chern class of the spacetime vanishes, implying that the spacetime is Calabi–Yau. More generally (2,2) theories have two complex structures and the B model exists when the first Chern classes of associated bundles sum to zero whereas the A model exists when the difference of the Chern classes is zero. In the Kähler case the two complex structures are the same and so the difference is always zero, which is why the A model always exists. There is no restriction on the number of dimensions of spacetime, other than that it must be even because spacetime is generalized Kähler. However, all correlation functions with worldsheets that are not spheres vanish unless the complex dimension of the spacetime is three, and so spacetimes with complex dimension three are the most interesting. This is fortunate for phenomenology, as phenomenological models often use a physical string theory compactified on a 3 complex-dimensional space. The topological string theory is not equivalent to the physical string theory, even on the same space, but certain supersymmetric quantities agree in the two theories. Objects A-model The topological A-model comes with a target space which is a 6 real-dimensional generalized Kähler spacetime. In the case in which the spacetime is Kähler, the theory describes two objects. There are fundamental strings, which wrap two real-dimensional holomorphic curves. Amplitudes for the scattering of these strings depend only on the Kähler form of the spacetime, and not on the complex structure. Classically these correlation functions are determined by the cohomology ring. There are quantum mechanical instanton effects which correct these and yield Gromov–Witten invariants, which measure the cup product in a deformed cohomology ring called the quantum cohomology. The string field theory of the A-model closed strings is known as Kähler gravity, and was introduced by Michael Bershadsky and Vladimir Sadov in Theory of Kähler Gravity. In addition, there are D2-branes which wrap Lagrangian submanifolds of spacetime. These are submanifolds whose dimensions are one half that of space time, and such that