Rotating membranes on G_2 manifolds, logarithmic anomalous dimensions and N=1 duality

Abstract

We show that the $E-S\sim \log S$ behaviour found for long strings rotating on $Ad{S}_5\times S^5$ may be reproduced by membranes rotating on $Ad{S}_4\times S^7$ and on a warped $Ad{S}_5$ M-theory solution. We go on to obtain rotating membrane 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 four dimensions. We study membrane configurations on $G_2$ holonomy backgrounds systematically, finding various other Energy-Charge relations. We end with some comments about strings rotating on warped backgrounds.

1+44 pages. Latex. No figures. Minor corrections to make all membrane configurations consistent. One configuration is now noncompact

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