Anomaly Cancellation And Abelian Gauge Symmetries In F-theory

TL;DR

This paper investigates anomaly cancellation in 4D F-theory compactifications with fluxes, revealing how geometric relations and fluxes ensure consistency of gauge symmetries and matter content.

Contribution

It provides a detailed analysis of anomaly cancellation mechanisms in F-theory, including the role of fluxes, geometric relations, and the Green-Schwarz mechanism, with explicit examples and comparisons to Type IIB.

Findings

F-theory fluxes automatically implement the Green-Schwarz mechanism.

Explicit geometric relations ensure anomaly cancellation in resolved Calabi-Yau fourfolds.

Comparison with Type IIB orientifold setups confirms the consistency of anomaly cancellation methods.

Abstract

We study 4D F-theory compactifications on singular Calabi-Yau fourfolds with fluxes. The resulting N=1 effective theories can admit non-Abelian and U(1) gauge groups as well as charged chiral matter. In these setups we analyze anomaly cancellation and the generalized Green-Schwarz mechanism. This requires the study of 3D N=2 theories obtained by a circle compactification and their M-theory duals. Reducing M-theory on resolved Calabi-Yau fourfolds corresponds to considering the effective theory on the 3D Coulomb branch in which certain massive states are integrated out. Both 4D gaugings and 3D one-loop corrections of these massive states induce Chern-Simons terms. All 4D anomalies are captured by the one-loop terms. The ones corresponding to the mixed gauge-gravitational anomalies depend on the Kaluza-Klein vector and are induced by integrating out Kaluza-Klein modes of the U(1) charged matter. In M-theory all Chern-Simons terms classically arise from G_4-flux. We find that F-theory fluxes implement automatically the 4D Green-Schwarz mechanism if non-trivial geometric relations for the resolved Calabi-Yau fourfold are satisfied. We confirm these relations in various explicit examples and elucidate the general construction of U(1) symmetries in F-theory. We also compare anomaly cancellation in F-theory with its analog in Type IIB orientifold setups.