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

TL;DR

The paper develops a transdimensional approach to determine the six-dimensional (1,0) effective action of F-theory on singular elliptically fibered Calabi–Yau threefolds by lifting to M-theory on the resolved CY3 and matching circle-reduced 6d supergravity to the M-theory reduction. It inserts a careful treatment of self-dual tensor fields, Green–Schwarz anomaly cancellation, and higher-curvature terms, and shows that certain one-loop Chern–Simons couplings arising from massive modes complete the duality with geometry. By analyzing the F-theory lift and the M-theory reduction on the resolved manifold, the authors extract the geometric data that encode 6d anomaly coefficients and the canonical 5d N=2 structure, including non-polynomial terms in the 5d function N^F interpreted as counterterms. The work reveals a precise correspondence between 6d anomaly data and classical topology in M-theory, augmented by circle-induced and KK-mode loop corrections, and it outlines future directions for non-Abelian tensor sectors, additional U(1)s, and full loop analyses.

Abstract

The six-dimensional effective action of F-theory compactified on a singular elliptically fibred Calabi-Yau threefold is determined by using an M-theory lift. The low-energy data are derived by comparing a circle reduction of a general six-dimensional (1,0) gauged supergravity theory with the effective action of M-theory on the resolved Calabi-Yau threefold. The derivation includes six-dimensional tensor multiplets for which the (anti-) self-duality constraints are imposed on the level of the five-dimensional action. The vector sector of the reduced theory is encoded by a non-standard potential due to the Green-Schwarz term in six dimensions. This Green-Schwarz term also contains higher curvature couplings which are considered to establish the full map between anomaly coefficients and geometry. F-/M-theory duality is exploited by moving to the five-dimensional Coulomb branch after circle reduction and integrating out massive vector multiplets and matter hypermultiplets. The associated fermions then generate additional Chern-Simons couplings at one-loop. Further couplings involving the graviphoton are induced by quantum corrections due to excited Kaluza-Klein modes. On the M-theory side integrating out massive fields corresponds to resolving the singularities of the Calabi-Yau threefold, and yields intriguing relations between six-dimensional anomalies and classical topology.