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

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.

15 pages. Minor changes, added references

References in corpus (2)

• Holographic Action for the Self-Dual Field
• Automorphic properties of (2, 0) theory on T6

Cited by in corpus (12)

• The $(2,0)$ superconformal bootstrap
• Anomaly polynomial of general 6d SCFTs
• On the Defect Group of a 6D SCFT
• Top Down Approach to 6D SCFTs
• On the 6d origin of discrete additional data of 4d gauge theories
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• The global anomalies of (2,0) superconformal field theories in six dimensions
• 6D SCFTs and Gravity
• The anomaly line bundle of the self-dual field theory
• The global gravitational anomaly of the self-dual field theory
• Generalized symmetry constraints on deformed 4d (S)CFTs