A scan for new N=1 vacua on twisted tori

TL;DR

This paper systematically searches for N=1 Minkowski vacua in type II string theories on twisted tori, discovering new solutions that are not dual to Calabi-Yau backgrounds and exploring their properties within generalized complex geometry.

Contribution

It provides the first examples of Minkowski vacua in supergravity on twisted tori that are not related to Calabi-Yau manifolds, including solutions requiring multiple intersecting sources.

Findings

Identified solutions T-dual to IIB backgrounds with self-dual flux

Constructed fully localized solutions for certain backgrounds

Discovered new solutions with intersecting sources needing smearing approximations

Abstract

We perform a systematic search for N=1 Minkowski vacua of type II string theories on compact six-dimensional parallelizable nil- and solvmanifolds (quotients of six-dimensional nilpotent and solvable groups, respectively). Some of these manifolds have appeared in the construction of string backgrounds and are typically called twisted tori. We look for vacua directly in ten dimensions, using the a reformulation of the supersymmetry condition in the framework of generalized complex geometry. Certain algebraic criteria to establish compactness of the manifolds involved are also needed. Although the conditions for preserved N=1 supersymmetry fit nicely in the framework of generalized complex geometry, they are notoriously hard to solve when coupled to the Bianchi identities. We find solutions in a large-volume, constant-dilaton limit. Among these, we identify those that are T-dual to backgrounds of IIB on a conformal T^6 with self-dual three-form flux, and hence conceptually not new. For all backgrounds of this type fully localized solutions can be obtained. The other new solutions need multiple intersecting sources (either orientifold planes or combinations of O-planes and D-branes) to satisfy the Bianchi identities; the full list of such new solution is given. These are so far only smeared solutions, and their localization is yet unknown. Although valid in a large-volume limit, they are the first examples of Minkowski vacua in supergravity which are not connected by any duality to a Calabi-Yau. Finally, we discuss a class of flat solvmanifolds that may lead to AdS_4 vacua of type IIA strings.