Spin chain from membrane and the Neumann-Rosochatius integrable system

TL;DR

This paper establishes a connection between membrane configurations in AdS_4 x S^7 and integrable spin chains, linking string theory, membrane dynamics, and the Neumann-Rosochatius integrable system.

Contribution

It introduces membrane solutions corresponding to SU(2) spin chains as limits of SU(3) chains, extending integrability insights from string to membrane frameworks.

Findings

Membrane configurations match the continuous limit of SU(2) spin chains.

Relationship between membrane dynamics and the Neumann-Rosochatius system is clarified.

Comparison of Lagrangians for string and membrane cases is provided.

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.