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We show that the $E-S \sim \log S$ behaviour found for long strings rotatingon $AdS_5\times S^5$ may be reproduced by membranes rotating on $AdS_4\timesS^7$ and on a warped $AdS_5$ M-theory solution. We go on to obtain rotatingmembrane configurations with the same $E-K \sim \log K$ relation on $G_2$holonomy backgrounds that are dual to ${\mathcal{N}}=1$ gauge theories in fourdimensions. We study membrane configurations on $G_2$ holonomy backgroundssystematically, finding various other Energy-Charge relations. We end with somecomments about strings rotating on warped backgrounds.Comment: 1+44 pages. Latex. No figures. Minor corrections to make all membrane  configurations consistent. One configuration is now noncompac

Rotating membranes onG2manifolds, logarithmic anomalous dimensions andN= 1 duality

Rotating membranes onG₂manifolds, logarithmic anomalous dimensions andN= 1 duality