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

TL;DR

This paper investigates the relationship between 4D supergravity theories and F-theory geometries, revealing how topological data and couplings in 4D theories mirror structures in 6D theories and are constrained by F-theory geometry.

Contribution

It establishes a detailed correspondence between F-theory topology and 4D supergravity data, extending known 6D structures to four dimensions and exploring implications for dualities and geometric constraints.

Findings

Topological axion-curvature couplings in 4D are characterized by vectors dual to axion shift symmetries.

F-theory geometry imposes constraints on 4D supergravity theories in the large-volume limit.

The correspondence illuminates heterotic-F-theory duality in 4D and 6D.

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.