Magnon-Like Dispersion Relation from M-Theory

TL;DR

This paper derives magnon-like dispersion relations from classical rotating membranes in M-theory backgrounds, extending string theory results to membrane solutions in $AdS_4\times S^7$ and $AdS_7\times S^4$.

Contribution

It presents the first membrane solutions in $AdS_4\times S^7$ with magnon dispersion relations and explores new conserved charge relations in $AdS_7\times S^4$.

Findings

Derived magnon-type dispersion relation in $AdS_4\times S^7$

Found new relations between conserved charges in $AdS_7\times S^4$

Extended string theory magnon results to membrane solutions

Abstract

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in $AdS_4\times S^7$ background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin case. In the appendix of the paper, we consider membrane solutions in $AdS_7\times S^4$, which give new relations between the conserved charges.