Quantizing Open Spin Chains with Variable Length: an example from Giant Gravitons

TL;DR

This paper develops a method to quantize an open spin chain with variable length, modeling Giant Gravitons in AdS/CFT, by mapping it to a bosonic lattice and using coherent states for semiclassical analysis.

Contribution

It introduces a novel quantization approach for variable-length open spin chains related to Giant Gravitons, connecting spin models to bosonic lattices and semiclassical string descriptions.

Findings

Mapped spin chain states to a bosonic lattice with boundary sources and sinks.

Demonstrated the Hamiltonian reproduces semiclassical open string dynamics.

Provided a framework for analyzing variable-length open spin chains in AdS/CFT.

Abstract

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of Giant Gravitons in the AdS/CFT correspondence. We show how to quantize the spin chain by mapping its states to a bosonic lattice of finite length with sources and sinks of particles at the boundaries. Using coherent states, we show how the Hamiltonian for the bosonic lattice gives the correct description of semiclassical open strings ending on Giant Gravitons.