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Six-dimensional (2, 0) theory can be defined on a large class ofsix-manifolds endowed with some additional topological and geometric data (i.e.an orientation, a spin structure, a conformal structure, and an R-symmetrybundle with connection). We discuss the nature of the object that generalizesthe partition function of a more conventional quantum theory. This object takesits values in a certain complex vector space, which fits together into thetotal space of a complex vector bundle (the `partition bundle') as the data onthe six-manifold is varied in its infinite-dimensional parameter space. In thiscontext, an important role is played by the middle-dimensional intermediateJacobian of the six-manifold endowed with some additional data (i.e. asymplectic structure, a quadratic form, and a complex structure). We define acertain hermitian vector bundle over this finite-dimensional parameter space.The partition bundle is then given by the pullback of the latter bundle by themap from the parameter space related to the six-manifold to the parameter spacerelated to the intermediate Jacobian.

The partition bundle of type A_{N-1} (2, 0) theory