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

TL;DR

This paper introduces a new decoupling limit of membranes that results in an integrable (1+2)-dimensional model, connecting membrane dynamics in specific supergravity backgrounds to classical integrability.

Contribution

It proposes a novel decoupling limit of membranes leading to an integrable model, linking supergravity backgrounds with classical integrability in a new regime.

Findings

Derivation of the integrable (1+2)-dimensional model from membrane limits.

Connection between supergravity backgrounds and classical integrability.

Identification of a scaling limit involving tension and relativistic effects.

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.