New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities

TL;DR

This paper constructs new explicit Spin(7) holonomy metrics that admit G2 holonomy reductions, revealing geometric dualities relevant to M-theory and IIA string theory, and explores their fibrations over Kahler and Eguchi-Hanson spaces.

Contribution

It introduces novel Spin(7) metrics with G2 reductions, expanding the known geometric structures and dualities in M-theory and string theory contexts.

Findings

Constructed explicit Spin(7) metrics with G2 reduction

Demonstrated Spin(7) to G2 to Kahler fibration pattern

Fibrations over Eguchi-Hanson instanton described

Abstract

IAs is well known, when D6 branes wrap a special lagrangian cycle on a non compact CY 3-fold in such a way that the internal string frame metric is Kahler there exists a dual description, which is given in terms of a purely geometrical eleven dimensional background with an internal metric of $G_2$ holonomy. It is also known that when D6 branes wrap a coassociative cycle of a non compact $G_2$ manifold in presence of a self-dual two form strength the internal part of the string frame metric is conformal to the $G_2$ metric and there exists a dual description, which is expressed in terms of a purely geometrical eleven dimensional background with an internal non compact metric of Spin(7) holonomy. In the present work it is shown that any $G_2$ metric participating in the first of these dualities necessarily participates in one of the second type. Additionally, several explicit Spin(7) holonomy metrics admitting a $G_2$ holonomy reduction along one isometry are constructed. These metrics can be described as $R$-fibrations over a 6-dimensional Kahler metric, thus realizing the pattern Spin(7) $\to G_2\to$ (Kahler) mentioned above. Several of these examples are further described as fibrations over the Eguchi-Hanson gravitational instanton and, to the best of our knowledge, have not been previously considered in the literature.