Magnon Bound States and the AdS/CFT Correspondence

TL;DR

This paper analyzes the spectrum of bound magnon states in the spin-chain model of planar N=4 SUSY Yang-Mills, revealing their exact dispersion relations, supersymmetric properties, and dual string theory descriptions across coupling regimes.

Contribution

It introduces the exact dispersion relation for multi-magnon bound states and connects these states to their string theory counterparts at strong coupling.

Findings

Bound states have an exact dispersion relation involving Q and p.

These states match poles in the exact S-matrix.

They are present at all coupling strengths and form supersymmetric representations.

Abstract

We study the spectrum of asymptotic states in the spin-chain description of planar N=4 SUSY Yang-Mills. In addition to elementary magnons, the asymptotic spectrum includes an infinite tower of multi-magnon bound states with exact dispersion relation, Delta-J_{1} = sqrt{Q^{2}+(lambda/pi^2)sin^2(p/2)}, where the positive integer Q is the number of constituent magnons. These states account precisely for the known poles in the exact S-matrix. Like the elementary magnon, they transform in small representations of supersymmetry and are present for all values of the 't Hooft coupling. At strong coupling we identify the dual states in semiclassical string theory.