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

TL;DR

This paper explores the mathematical structure of the partition function of six-dimensional (2,0) theories, framing it as a complex vector bundle over a parameter space linked to the intermediate Jacobian of the six-manifold.

Contribution

It introduces the concept of a partition bundle for (2,0) theories and describes its construction via the intermediate Jacobian and associated vector bundles.

Findings

The partition function generalizes to a section of a complex vector bundle.

The partition bundle is constructed as a pullback from a hermitian vector bundle.

The intermediate Jacobian plays a central role in the bundle's structure.

Abstract

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