Finite-size effects of Membranes on AdS_4 x S_7

TL;DR

This paper studies finite-size effects of membranes in AdS_4 x S^7, identifying specific states and their energy relations, and connects these to integrable models relevant to the dual ABJM theory.

Contribution

It introduces finite-size membrane solutions in AdS_4 x S^7 and links them to integrable models, providing new insights into the dual ABJM theory.

Findings

Identified giant magnon and single spike states on membranes.

Derived finite-size corrections to energy-charge relations.

Connected membrane solutions to complex sine-Gordon model.

Abstract

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. 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.