Finite-size effects of membranes onAdS₄×S₇

Abstract

We consider semi-classical solutions of membranes on the AdS 4 × S 7 background. 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.

Neumann-Rosochatius system for strings in ABJ model

“…to the NR system has been quite useful in unravelling new relationships between the integrable structures of the two sides of the AdS/CFT duality [18,[23][24][25][26][27]. Such an approach has previously been used to study the finite size effect to the giant magnon (GM) solutions in AdS 4 × S 7 background [28]. It is worth emphasizing that the NR integrable system is very effective in dealing with the classical strings in R t × CP 3 .…”

“…It is worth emphasizing that the NR integrable system is very effective in dealing with the classical strings in R t × CP 3 . Indeed in [28], the string dynamics on AdS 4 × CP 3 has been studied by using the NR integrable system. The dispersion relation and subsequently the finite size effects for the giant magnon and single spike solutions for the string on R t ×CP 3 with two angular momenta have been studied in detail.…”

“…The dispersion relation and subsequently the finite size effects for the giant magnon and single spike solutions for the string on R t ×CP 3 with two angular momenta have been studied in detail. In this article, we wish to extend the analysis presented in [28] to the case of spinning closed strings in AdS 4 ×CP 3 in the presence of B N S holonomy.…”

Finite-size effect of the dyonic giant magnons inN=6super Chern-Simons theory

“…For the N ¼ 6 CS theory, both methods have been implemented to compute the effect for a giant magnon (GM) which moves symmetrically in SUð2Þ Â SUð2Þ subspace of CP 3 [25]. See [26][27][28][29][30] for subsequent developments on the finite-size effects of the AdS 4 =CFT 3 from the string/membrane side.…”

Wilson loops in 3d QFT from D-branes in AdS4×CP3

“…and the four-form field 6) where dΩ AdS 4 is unit volume form of the AdS 4 . There exist freedom in determination of the three-form C (3) and we choose following one…”