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

Abstract

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.

38 pages. v3: Corrections in the discussion of the global anomaly cancellation in type IIB sugra. Typos corrected

References in corpus (9)

• Holographic Action for the Self-Dual Field
• The M-theory 3-form and E8 gauge theory
• Type II Actions from 11-Dimensional Chern-Simons Theories
• Geometric quantization and the metric dependence of the self-dual field theory
• The anomaly line bundle of the self-dual field theory
• Conformal invariants of twisted Dirac operators and positive scalar curvature
• Canonical quadratic refinements of cohomological pairings from functorial lifts of the Wu class
• Gauss Sums in Algebra and Topology
• Global anomalies and chiral p-forms

Cited by in corpus (10)

• Anomaly polynomial of general 6d SCFTs
• IIB flux non-commutativity and the global structure of field theories
• The anomaly that was not meant IIB
• Remarks on the Green-Schwarz terms of six-dimensional supergravity theories
• A Modern Point of View on Anomalies
• Ramond-Ramond fields and twisted differential K-theory
• Anomaly inflow and $p$-form gauge theories
• 4d N=1 from 6d D-type N=(1,0)
• Some comments on 6d global gauge anomalies
• Global gravitational anomalies and transport