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IAs is well known, when D6 branes wrap a special lagrangian cycle on a noncompact CY 3-fold in such a way that the internal string frame metric is Kahlerthere exists a dual description, which is given in terms of a purelygeometrical eleven dimensional background with an internal metric of $G_2$holonomy. It is also known that when D6 branes wrap a coassociative cycle of anon compact $G_2$ manifold in presence of a self-dual two form strength theinternal part of the string frame metric is conformal to the $G_2$ metric andthere exists a dual description, which is expressed in terms of a purelygeometrical eleven dimensional background with an internal non compact metricof Spin(7) holonomy. In the present work it is shown that any $G_2$ metricparticipating in the first of these dualities necessarily participates in oneof the second type. Additionally, several explicit Spin(7) holonomy metricsadmitting a $G_2$ holonomy reduction along one isometry are constructed. Thesemetrics 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 theEguchi-Hanson gravitational instanton and, to the best of our knowledge, havenot been previously considered in the literature.

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