Type II compactifications on manifolds with SU(2) x SU(2) structure

TL;DR

This paper investigates type II string theory compactifications on SU(2) x SU(2) structure manifolds, revealing differences from SU(3) x SU(3) cases and describing their moduli spaces using generalized geometry and exceptional generalized geometry.

Contribution

It introduces a detailed analysis of SU(2) x SU(2) structure compactifications, highlighting the absence of interpolating structures and formulating the moduli space within exceptional generalized geometry.

Findings

No dynamical SU(2) x SU(2) structure interpolates between SU(2) and identity structures.

Moduli spaces match expectations from N=4 supergravity.

Framework incorporates scalar degrees of freedom from Ramond-Ramond sector.

Abstract

We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive the structure of their moduli spaces. We show that in contrast to SU(3) x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures in the context of exceptional generalized geometry which makes the U-duality group manifest and naturally incorporates the scalar degrees of freedom arising in the Ramond-Ramond sector. Via this formalism we derive the structure of the moduli spaces as it is expected from N=4 supergravity.