Finite-size effects of Membranes on AdS_4 x S_7

Understand

We consider semi-classical solution of membranes on the AdS_4 x S^7.

• This is supposed to be dual to the N=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.