Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality

TL;DR

This paper demonstrates that an N=2 superconformal Sp(N) gauge theory with matter, dual to an open+closed string system in the plane‑wave limit, contains integrable spin‑chain structures: a closed SO(6) chain for the bulk and an open SU(3) chain with boundary terms for the open string sector. By using the R‑matrix and boundary K‑matrix formalism, the authors show the open chain is integrable and solve its algebraic Bethe ansatz equations to reproduce the free open plane‑wave string spectrum for configurations with a few impurities. They carefully identify the boundary conditions that reflect string endpoints, analyze simple impurity configurations (Z′ and W insertions, bound impurities), and discuss the thermodynamic limit and more general root structures, outlining future work on string interactions and complex roots. The results provide a concrete, exact bridge between gauge‑theory operator mixing and open string spectra in a plane‑wave background, highlighting the role of integrability in open/closed string sectors and offering a framework to explore beyond‑BMN regimes.

Abstract

We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N=4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.

Figures (1)

• Figure 1: One-loop planar diagrams involving quarks at boundary. Here the solid lines denote chiral fields $(Z,Z',W)$ and dash lines denote the chiral field $(\tilde{q},q)$. It should be noticed that $Z,\;Z'$ contribution is absent in the third graph.