Description
Anomalies in 6d theories are cancelled by a generalized Green-Schwarz mechanism.
This should not only be true for local anomalies but also for global anomalies that in particular arise from discrete 0-form gauge symmetries.
Anomaly inflow further relates these discrete 6d anomalies to 't Hooft anomalies of corresponding global discrete symmetries on 2d worldsheet theories of non-critical strings.
The 't Hooft anomalies of these global symmetries can in turn be measured as a failure of modularity of the corresponding orbifold partition functions.
We will argue that in F-theory the elliptic genera with twisted boundary conditions are encoded in the topological string partition functions on various torus fibrations, that share the same Jacobian fibration, as well as certain non-commutative crepant resolutions.
The corresponding modular properties will allow us to obtain a precise geometric expression for the global anomaly in terms of a height pairing of a multi-section.
At the example of theories with Z3 symmetry we demonstrate that different values for the global anomaly distinguish theories that have otherwise identical massless spectra.
The talk is based on work in progress with M. Dierigl and P. Oehlmann.
