The Manakov-Zakharov-Ward model as an integrable decoupling limit of the membrane

Abstract

A novel decoupling limit of the membrane is proposed, leading to the $(1+2)$-dimensional classically integrable model originally introduced by Manakov, Zakharov, and Ward. This limit is the large-wrapping regime of a membrane propagating toy background of the form ${\mathbb{R}}_t\times T^2\times G$ subject to scaling limit, where $G$ is a Lie group and the geometry is supported by a four-form flux. Such toy backgrounds can arise from consistent eleven-dimensional supergravity solutions, exemplified by the uplift of the pure NSNS AdS${}_3\times$ S${}^3\times$ T${}^4$ background. The scaling limit can be interpreted as similtaneous small tension and non- or hyper-relativistic limit.

5 pages + appendix, version 3, v3: new implementation of the limit at the level of the action included in section 2; v2: added references, typos mistake in eq. (1.3) and follow-up mistakes in calculation of the limit corrected, modified presentation of the non-Lorentzian interpretation