Spin chain from membrane and the Neumann-Rosochatius integrable system

Abstract

We find membrane configurations in AdS_4 x S^7, which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS_5 x S^5. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.Comment: LaTeX, 16 pages, no figures; v2: 17 pages, title changed, explanations and references added; v3: more explanations added; v4: typos fixed, to appear in Phys. Rev.

Finite-size effects of membranes onAdS4×S7

“…The NR system has been proposed for the string theory on AdS 5 × S 5 in [21,22,23]. It was also established that they can reproduce the continuous limit of the integrable SU(2) spin chain [24]. (See also [25].)…”

Integrable systems from membranes on AdS4 × S7

“…Here, we are interested in answering the question: is it possible to reproduce this type of string/spin chain correspondence from membranes on eleven dimensional curved backgrounds? It turns out that the answer is positive at least for the case of M2-branes on AdS 4 × S 7 , as we will show below [6].…”

“…It turns out that the answer is positive at least for the case of M2-branes on AdS 4 × S 7 , as we will show below [6]. We will use our initial membrane embedding and fix…”

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

“…Moreover, the single spike solutions of [41] can be reproduced also from membranes on AdS 4 × S 7 [42]. In addition, one can consider the correspondence between the Neumann and Neumann-Rosochatius integrable systems arising from membranes and the continuous limit of integrable spin chains at the level of actions, as is done in [43]. Besides, it is interesting to clarify the relationship with the constant radii solutions for membranes on AdS 4 × S 7 found in [40].…”