Magnon-Like Dispersion Relation from M-Theory

Abstract

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in $Ad{S}_4\times S^7$ 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 $Ad{S}_7\times S^4$, which give new relations between the conserved charges.

16 pages, typos corrected; V3: New section and comments added, to appear in Nucl. Phys. B

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• Single spike solutions for strings on S2 and S3
• Dressing the Giant Magnon II
• Fat Magnon
• Scattering of single spikes
• Dual Spikes; New Spiky String Solutions
• Finite-size effects of Membranes on AdS_4 x S_7
• On the anatomy of multi-spin magnon and single spike string solutions
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• On the multi-spin magnon and spike solutions from membranes
• Giant Magnons and Spiky Strings on S^3 with B-field
• A note on two-spin magnon-like energy-charge relations from M-theory viewpoint
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• Carroll membranes
• The AdS_5 x S^5 superstrings in the generalized light-cone gauge
• Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
• 2D Heisenberg model from rotating membrane
• Rotating Membranes in AdS_4xM^{1,1,1}