2D Heisenberg model from rotating membrane

TL;DR

This paper explores how a rotating membrane in M-theory's AdS_4 x S^7 background simplifies to well-known spin models in the fast limit, extending the correspondence to higher-dimensional branes.

Contribution

It demonstrates the reduction of tensionless membranes to spin chain models and generalizes the correspondence to higher-dimensional branes with anisotropy and magnetic fields.

Findings

Membrane worldvolume reduces to XXX_1/2 spin chain or SU(2) Heisenberg model in the fast limit.

Established the membrane-spin model correspondence for higher-dimensional branes.

Extended the model to include anisotropy and external magnetic fields.

Abstract

We study a rotating probe membrane in S^3 inside AdS_4 x 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.