Neumann and Neumann-Rosochatius integrable systems from membranes onAdS4×S7

Bozhilov, P.

doi:10.1088/1126-6708/2007/08/073

Cited by 22 publications

(15 citation statements)

References 48 publications

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“…One direction is to study the reduced sine-Gordon system discussed in Appendix A. Another direction is to study in detail classical membrane spectrum in AdS 4 × S 7 /Z k for general k, and carefully take the limit k → ∞ limit [77,78,79,80]. We hope to revisit such problems in future.…”

Section: Summary and Discussionmentioning

confidence: 99%

Giant Magnons on ℂℙ³by dressing method

Suzuki¹

2009

J. High Energy Phys.

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We consider classical string spectrum of R t × CP 3 , and construct a family of solutions with residual SU(2) symmetry by the dressing method on SU(4)/U(3) sigma model. All of them obey the square-root type dispersion relation often found in the theory with su(2|2) symmetry. A single dyonic giant magnon is not found in this approach. rsuzuki@maths.tcd.ieAn effective field theory of coincident membranes with N = 8 superconformal symmetry in 1+2 dimensions is proposed by Bagger, Lambert, and Gustavsson (BLG) based on three-algebra [1,2,3]. Aharony, Bergman, Jafferis and Maldacena (ABJM) proposed an N = 6 superconformal Chern-Simons-matter theory with a tunable coupling constant λ = N/k by generalizing the BLG theory to incorporate U(N) k × U(N) −k symmetry group -which coincides with the special case of [4,5] -and argued that their model at the 't Hooft limit is dual to type IIA superstring theory on the AdS 4 × CP 3 background [6,7].The IIA on AdS 4 × CP 3 is less supersymmetric than the IIB on AdS 5 × S 5 , which was conjectured to be dual to N = 4 super Yang-Mills in 1+3 dimensions [8]. Integrability has provided us a powerful tool to study the AdS 5 /CFT 4 correspondence, and a matter of central concern is whether and how similar techniques are applied to the AdS 4 /CFT 3 case.Despite huge and rapid progress on this subject, no conclusive answer has been given. Looking on the positive side, one finds the integrability of two-loop Hamiltonian in ABJM model [9,10,11,12], classical integrability of superstring action (except for a subtle issue concerning strings in AdS 4 ) [13,14,15], 1 and the proposal of all-loop Bethe Ansatz [20,21,22,23], which is consistent with near-plane wave limit of string theory [24,25,26,27,28]. On the negative side, one finds disagreement between the one-loop energy of folded or circular string, and the proposed Bethe Ansatz [29,30,31,32,33].More data, especially the examples that are not found in AdS 5 × S 5 case, are necessary to refine our understanding of the AdS 4 /CFT 3 duality and its integrability [34,35,36,37,38,39,40,41,42]. A good starting point will be to reconsider the correspondence between magnons in the asymptotic spin chain and giant magnon solutions on the decompactified worldsheet [43,44,45,25], as one could expect nice examples of the duality owing to the su(2|2) symmetry.The description by algebraic curve tells the classical string spectrum and its dispersion in a simple way [46,47]. Yet, to obtain further information such as (semiclassical) quantization and scattering [48,49,50,51,52], 2 it is useful to construct an explicit profile of the corresponding string solution.The aim of this paper is to construct the explicit profile of classical strings on which only the existence and the dispersion have been known so far by means of algebraic curve. The relationship between a string solution and an algebraic curve is not explicit in general, so we have to construct the classical string solution from scratch. This sort of problem is quite difficult in general, due to th...

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Section: Summary and Discussionmentioning

confidence: 99%

Giant Magnons on ℂℙ³by dressing method

Suzuki¹

2009

J. High Energy Phys.

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“…The application of the NR system to the SS in S 3 has been worked out in [28], the most general case of GM and SS has been considered in [29] and to the finite-size effects in [30]. The NR integrable system in AdS 4 /CF T 3 was used to find the GM solution for the membrane on AdS 4 × S 7 [31] and to compute the finite-size effects in [18]. In this article we apply this system to the strings moving in the R t × CP 3 background.…”

Section: Jhep09(2008)017mentioning

confidence: 99%

Neumann-Rosochatius integrable system for strings onAdS₄× ℂℙ³

Ahn

Bozhilov

Rashkov

2008

J. High Energy Phys.

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We use the reduction of the string dynamics on AdS 4 × CP 3 to the Neumann-Rosochatius integrable system. All constraints can be expressed simply in terms of a few parameters. We analyze the giant magnon and single spike solutions on R t × CP 3 with two angular momenta in detail and find the energy-charge relations. The finite-size effects of the giant magnon and single spike solutions are analyzed.

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“…In the Ref. [23], the author found several types of membrane embedding into the AdS 4 × S 7 background, which are related to the Neumann and Neumann-Rosochatius integrable systems. Our result supports his conjecture that there might have various kinds of integrable system dual to membranes in the M-theory.…”

Section: Discussionmentioning

confidence: 99%

2D Heisenberg model from rotating membrane

Wen¹

2008

Nuclear Physics B

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We study a rotating probe membrane in S 3 inside AdS 4 × S 7 background of M-theory. With (partial) gauge fixing, we show that in the fast limit the worldvolume of tensionless membrane reduces to either the XXX 1/2 spin chain or the two-dimensional SU (2) Heisenberg spin model.Later we introduce the anisotropy and couple it to the external magnetic field. We also establish the correspondence for higher dimensional (D)p-branes.

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Neumann and Neumann-Rosochatius integrable systems from membranes onAdS₄×S⁷

Cited by 22 publications

References 48 publications

Giant Magnons on ℂℙ³by dressing method

Giant Magnons on ℂℙ³by dressing method

Neumann-Rosochatius integrable system for strings onAdS₄× ℂℙ³

2D Heisenberg model from rotating membrane

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Neumann and Neumann-Rosochatius integrable systems from membranes onAdS4×S7

Cited by 22 publications

References 48 publications

Giant Magnons on ℂℙ3by dressing method

Giant Magnons on ℂℙ3by dressing method

Neumann-Rosochatius integrable system for strings onAdS4× ℂℙ3

2D Heisenberg model from rotating membrane

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Neumann and Neumann-Rosochatius integrable systems from membranes onAdS₄×S⁷

Giant Magnons on ℂℙ³by dressing method

Giant Magnons on ℂℙ³by dressing method

Neumann-Rosochatius integrable system for strings onAdS₄× ℂℙ³