Anomalous Dimensions of Heavy Operators from Magnon Energies

TL;DR

This paper investigates the anomalous dimensions of heavy operators in gauge theory by analyzing magnon energies in open spin chains, revealing boundary effects, symmetry constraints, and integrability breaking.

Contribution

It provides a detailed computation of magnon boundary scattering matrices and explores how boundary conditions affect integrability in open spin chains.

Findings

Quantitative agreement between gauge theory anomalous dimensions and string energies.

Computed boundary reflection/scattering matrix element at weak coupling.

Found that boundary conditions break integrability by violating the boundary Yang-Baxter equation.

Abstract

We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. The anomalous dimensions computed in the gauge theory are in complete quantitative agreement with energies computed in the dual string theory. The comparison makes use of a description in terms of magnons, generalizing results for a single maximal giant graviton. The symmetries of the problem determine the structure of the magnon boundary reflection/scattering matrix up to a phase. We compute a reflection/scattering matrix element at weak coupling and verify that it is consistent with the answer determined by symmetry. We find the reflection/scattering matrix does not satisfy the boundary Yang-Baxter equation so that the boundary condition on the open spin chain spoils integrability. We also explain the interpretation of the double coset ansatz in the magnon language.