Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds

The 6d effective action of F-theory compactified on an elliptically fibred Calabi-Yau threefold is determined using an M-theory lift. The non-Abelian gauge theory arises on a stack of seven-branes located on the singularities of the threefold. The gauge theory is analysed in the 5d Coulomb branch by resolving the Calabi-Yau threefold. The reduction includes an arbitrary number of 6d tensor multiplets for which the self- and anti-self duality constraints can be imposed in the 5d M-theory set-up. Higher curvature terms are crucial for anomaly cancellation in six dimensions, and are obtained from corrections to the 11d supergravity action. The chiral spectrum in a 6d supergravity theory is linked to the form of the Green-Schwarz couplings via anomalies. We find that these data are encoded in the 5d effective action via one loop corrections.