3d N=1 effective supergravity and F-theory from M-theory on fourfolds

TL;DR

This paper analyzes 3d N=1 supergravity arising from M-theory compactified on Calabi-Yau fourfolds, deriving the effective theory and exploring its F-theory duals with circle fluxes that break 4d Poincaré invariance.

Contribution

It provides a detailed derivation of the 3d N=1 effective supergravity from M-theory on fourfolds and explores the F-theory duals with circle fluxes.

Findings

The mass spectrum includes the volume modulus and axions from the three-form.

The moduli-space metric is locally hyperbolic.

F-theory duals generally involve circle fluxes breaking 4d Poincaré invariance.

Abstract

We consider 3d N=1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions. We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N=1 theory in the large-volume limit up to quartic fermion terms. We show that in general it is an ungauged N=1 supergravity of the form expected from 3d supersymmetry. In particular the massless bosonic fields consist of the volume modulus and the axions originating from the eleven-dimensional three-form, while the moduli-space metric is locally isometric to hyperbolic space. We consider the F-theory interpretation of the 3d N=1 M-theory vacua in the light of the F-theory effective action approach. We show that these vacua generally have F-theory duals with circle fluxes, thus breaking 4d Poincar\'e invariance.