Finite-size effects of Membranes on AdS_4 x S_7

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.

References added, typos fixed, acknowledgement added; 25 pages

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Cited by in corpus (24)

• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• Spinning strings at one-loop in AdS_4 x P^3
• Anomalous radius shift in AdS(4)/CFT(3)
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• Three-point Correlation functions of Giant magnons with finite size
• Superstrings on AdS_4 x CP^3 from Supergravity
• A note on the reduction of the AdS4 x CP3 string sigma model
• Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory
• Dressed Giant Magnons on CP^3
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• Wilson Loops in 3d QFT from D-branes in AdS(4) x CP**3
• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
• On thermodynamics of N=6 superconformal Chern-Simons theories at strong coupling
• Large-Spin Expansions of GKP Strings
• Stringy Membranes in AdS/CFT
• M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds
• Rotating Membranes in AdS_4xM^{1,1,1}
• Neumann-Rosochatius system for strings in ABJ Model
• Probing Non-Toric Geometry with Rotating Membranes
• Finite size effect from classical strings in $Ad{S}_3\times S^3$ with NS-NS flux
• Finite Size Effect from Classical Strings in deformed AdS${}_3\times$ S${}^3$
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes
• P-Branes Dynamics, AdS/CFT and Correlation Functions