Finite-size effects of membranes on AdS 4 × S 7

Abstract

We consider semi-classical solutions of membranes on the AdS 4 × S 7 background. This is supposed to be dual to the = 6 super Chern-Simons theory with k = 1 in a planar limit recently proposed by Aharony, Bergmann, Jafferis, and Maldacena (ABJM). We have identified giant magnon and single spike states on the membrane by reducing them to the Neumamm - Rosochatius integrable system. We also connect these to the complex sine-Gordon integrable model. Based on this approach, we find finite-size membrane solutions and obtain their images in the complex sine-Gordon system along with the leading finite-size corrections to the energy-charge relations.