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

TL;DR

This paper demonstrates that logarithmic energy-charge relations observed in string theory can be extended to membranes on G_2 manifolds, revealing new dualities and configurations in M-theory and four-dimensional N=1 gauge theories.

Contribution

It introduces rotating membrane solutions on G_2 holonomy backgrounds that reproduce known energy-charge relations and explores their implications for dual N=1 gauge theories.

Findings

Membranes on G_2 backgrounds exhibit E-K ~ log K relations.

Rotating membranes on warped AdS_5 solutions also show similar behavior.

Various other energy-charge relations are identified on G_2 holonomy backgrounds.

Abstract

We show that the $E-S \sim \log S$ behaviour found for long strings rotating on $AdS_5\times S^5$ may be reproduced by membranes rotating on $AdS_4\times S^7$ and on a warped $AdS_5$ 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.