Generalized N=1 and N=2 structures in M-theory and type II orientifolds

TL;DR

This paper explores how M-theory and type IIA string theory reductions to four dimensions with N=1 and N=2 supersymmetry can be understood through Exceptional Generalized Geometry, deriving effective couplings and analyzing orientifold projections.

Contribution

It introduces a unified framework using EGG to describe N=1 and N=2 reductions, computing key couplings and potentials, and analyzing orientifold actions and projections.

Findings

Derived N=1 and N=2 couplings including Kahler and hyper-Kahler potentials.

Connected M-theory and type IIA reductions via EGG structures.

Analyzed orientifold actions and projections, including new U-dual orientifolds.

Abstract

We consider M-theory and type IIA reductions to four dimensions with N=2 and N=1 supersymmetry and discuss their interconnection. Our work is based on the framework of Exceptional Generalized Geometry (EGG), which extends the tangent bundle to include all symmetries in M-theory and type II string theory, covariantizing the local U-duality group E7. We describe general N=1 and N=2 reductions in terms of SU(7) and SU(6) structures on this bundle and thereby derive the effective four-dimensional N=1 and N=2 couplings, in particular we compute the Kahler and hyper-Kahler potentials as well as the triplet of Killing prepotentials (or the superpotential in the N=1 case). These structures and couplings can be described in terms of forms on an eight-dimensional tangent space where SL(8) contained in E7 acts, which might indicate a description in terms of an eight-dimensional internal space, similar to F-theory. We finally discuss an orbifold action in M-theory and its reduction to O6 orientifolds, and show how the projection on the N=2 structures selects the N=1 ones. We briefly comment on new orientifold projections, U-dual to the standard ones.