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

TL;DR

This paper explores the integrable structures of an N=2 superconformal Sp(N) Yang-Mills theory with matter, revealing how open and closed string sectors relate to integrable spin chains and matching string spectra.

Contribution

It identifies the integrable open spin chain boundary conditions corresponding to string boundary conditions and solves the algebraic Bethe ansatz equations for open strings in the plane-wave background.

Findings

Open string sector described by an integrable SU(3) open spin chain.

Solutions to ABAE match free open string spectrum in plane-wave background.

Boundary conditions correspond to string boundary conditions.

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.