Spin Chain with Magnetic Field and Spinning String in Magnetic Field Background

TL;DR

This paper explores the relationship between fast-moving strings in magnetic Melvin backgrounds and deformed spin chain models, revealing how external magnetic fields deform the spin vectors on curved surfaces.

Contribution

It demonstrates that the effective string sigma model corresponds to a deformed spin chain with magnetic field, extending understanding of string-spin chain dualities in deformed backgrounds.

Findings

Spin vectors are deformed on two-sphere or hyperboloid surfaces.

The deformation depends on the string's spinning direction.

The property is general for strings in similar deformed backgrounds.

Abstract

We analyze the fast-moving string in the magnetic Melvin field background and find that the associated effective Lagrangian of string sigma model describes the spin chain model with external magnetic field. The spin vector in the spin chain has been properly deformed and is living on the deformed two-sphere or deformed two-dimensional hyperboloid, depending on the direction around which the string is spinning. We describe in detail the characters of spin deformation and, in particular, see that this is a general property for a string moving in a class of deformed background.