G(2) Holonomy Spaces from Invariant Three-Forms

TL;DR

This paper constructs new G(2) holonomy metrics relevant for M-theory compactifications, using a systematic approach based on torsion-free G(2) structures defined by closed and co-closed three-forms.

Contribution

It introduces novel G(2) metrics related to string theory brane configurations, employing a practical formalism of three-forms for their construction.

Findings

New G(2) metrics related to conifold transitions

Application of three-form formalism for metric construction

Relevance to M-theory compactifications

Abstract

We construct several new G(2) holonomy metrics that play an important role in recent studies of geometrical transitions in compactifications of M-theory to four dimensions. In type IIA string theory these metrics correspond to D6 branes wrapped on the three-cycle of the deformed conifold and the resolved conifold with two-form RR flux on the blown-up two-sphere, which are related by a conifold transition. We also study a G(2) metric that is related in type IIA to the line bundle over S^2 x S^2 with RR two-form flux. Our approach exploits systematically the definition of torsion-free G(2) structures in terms of three-forms which are closed and co-closed. Besides being an elegant formalism this turns out to be a practical tool to construct G(2) holonomy metrics.