M2-brane Perspective on N=6 Super Chern-Simons Theory at Level k

TL;DR

This paper explores M2-brane configurations in the ABJM theory's dual M-theory background, deriving exact solutions and dispersion relations that depend explicitly on the Chern-Simons level k.

Contribution

It provides explicit giant magnon and single spike solutions for membranes in AdS_4 x S^7/Z_k, connecting membrane dynamics to integrable models and finite-size effects.

Findings

Derived exact membrane solutions in AdS_4 x S^7/Z_k.

Obtained dispersion relations with finite-size corrections.

Connected membrane configurations to the Neumann-Rosochatius integrable model.

Abstract

Recently, O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena (ABJM) proposed three-dimensional super Chern-Simons-matter theory, which at level k is supposed to describe the low energy limit of N M2-branes. For large N and k, but fixed 't Hooft coupling \lambda=N/k, it is dual to type IIA string theory on AdS_4 x CP^3. For large N but finite k, it is dual to M theory on AdS_4 x S^7/Z_k. In this paper, relying on the second duality, we find exact giant magnon and single spike solutions of membrane configurations on AdS_4 x S^7/Z_k by reducing the system to the Neumann-Rosochatius integrable model. We derive the dispersion relations and their finite-size corrections with explicit dependence on the level k.