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The six-dimensional effective action of F-theory compactified on a singularelliptically fibred Calabi-Yau threefold is determined by using an M-theorylift. The low-energy data are derived by comparing a circle reduction of ageneral six-dimensional (1,0) gauged supergravity theory with the effectiveaction of M-theory on the resolved Calabi-Yau threefold. The derivationincludes six-dimensional tensor multiplets for which the (anti-) self-dualityconstraints are imposed on the level of the five-dimensional action. The vectorsector of the reduced theory is encoded by a non-standard potential due to theGreen-Schwarz term in six dimensions. This Green-Schwarz term also containshigher curvature couplings which are considered to establish the full mapbetween anomaly coefficients and geometry. F-/M-theory duality is exploited bymoving to the five-dimensional Coulomb branch after circle reduction andintegrating out massive vector multiplets and matter hypermultiplets. Theassociated fermions then generate additional Chern-Simons couplings atone-loop. Further couplings involving the graviphoton are induced by quantumcorrections due to excited Kaluza-Klein modes. On the M-theory side integratingout massive fields corresponds to resolving the singularities of the Calabi-Yauthreefold, and yields intriguing relations between six-dimensional anomaliesand classical topology.

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