The global anomaly of the self-dual field in general backgrounds

Understand

We prove a formula for the global gravitational anomaly of the self-dual field theory in the presence of background gauge fields, assuming the results of arXiv:1110.4639.

• Along the way, we also clarify various points about the self-dual field theory.
• In particular, we give a general definition of the theta characteristic entering its partition function and settle the issue of its possible metric dependence.
• We treat the cohomological version of type IIB supergravity as an example of the formalism: a mixed gauge-gravitational global anomaly, occurring when the B-field and Ramond-Ramond 2-form gauge fields have non-trivial Wilson lines, cancels provided a certain cobordism group vanishes.