The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua

Understand

We study the structure of gauge and gravitational anomalies in 2d N=(0,2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds.

• Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory.
• We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms.
• These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon.