M2-brane perspective on N = 6 super Chern-Simons theory at level k

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 λ = N/k, it is dual to type IIA string theory on AdS₄ × ³. For large N but finite k, it is dual to M theory on AdS₄ × S⁷/Z_k. In this paper, relying on the second duality, we find exact giant magnon and single spike solutions of membrane configurations on AdS₄ × 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.