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

TL;DR

This paper derives the six-dimensional effective action of F-theory on elliptically fibred Calabi-Yau threefolds using M-theory, revealing deep links between anomalies, geometry, and quantum corrections.

Contribution

It provides a detailed derivation of the 6D F-theory effective action via M-theory on resolved Calabi-Yau threefolds, including anomaly and higher curvature couplings.

Findings

Relation between anomaly coefficients and Calabi-Yau geometry

Quantum corrections induce Chern-Simons couplings

Resolution of singularities corresponds to integrating out massive fields

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.