Structure in 6D and 4D N=1 supergravity theories from F-theory

TL;DR

The work builds a detailed bridge between F-theory geometry and four-dimensional N=1 supergravity, mirroring the 6D story by connecting axion–curvature couplings to canonical/base-divisor data of the F-theory geometry. It shows how in the large-volume limit the 4D action encodes: (i) the complex structure and Kähler data via axion couplings to R^2 and F^2, (ii) the gauge sector through f_A and tau, and (iii) the D3/tadpole and chiral spectra through G4 flux and Theta matrices. The paper also develops a robust heterotic/F-theory dual dictionary in 4D, linking base twists and divisor classes to heterotic bundle data, and outlines geometrical constraints that must be satisfied by viable 4D F-theory vacua. Overall, it provides a framework to infer global geometry from 4D low-energy data in the large-volume regime and highlights open questions related to fluxes and off-shell moduli beyond this limit.

Abstract

We explore some aspects of 4D supergravity theories and F-theory vacua that are parallel to structures in the space of 6D theories. The spectrum and topological terms in 4D supergravity theories correspond to topological data of F-theory geometry, just as in six dimensions. In particular, topological axion-curvature squared couplings appear in 4D theories; these couplings are characterized by vectors in the dual to the lattice of axion shift symmetries associated with string charges. These terms are analogous to the Green-Schwarz terms of 6D supergravity theories, though in 4D the terms are not generally linked with anomalies. We outline the correspondence between F-theory topology and data of the corresponding 4D supergravity theories. The correspondence of geometry with structure in the low-energy action illuminates topological aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of an F-theory realization also places geometrical constraints on the 4D supergravity theory in the large-volume limit.