N=1 vacua in Exceptional Generalized Geometry

TL;DR

This paper investigates N=1 Minkowski vacua in type II string theory compactifications using exceptional generalized geometry, deriving differential equations for structures that encode fluxes and moduli, and identifying conditions for vacua.

Contribution

It formulates the differential conditions for N=1 vacua within exceptional generalized geometry, including a U-duality covariant twisted differential operator.

Findings

Derived differential equations for EGG structures

Identified a U-duality covariant twisted differential operator

Established conditions for N=1 vacua in EGG framework

Abstract

We study N=1 Minkowski vacua in compactifications of type II string theory in the language of exceptional generalized geometry (EGG). We find the differential equations governing the EGG analogues of the pure spinors of generalized complex geometry, namely the structures which parameterize the vector and hypermultiplet moduli spaces of the effective four-dimensional N=2 supergravity obtained after compactification. In order to do so, we identify a twisted differential operator that contains NS and RR fluxes and transforms covariantly under the U-duality group, E7(7). We show that the conditions for N=1 vacua correspond to a subset of the structures being closed under the twisted derivative.