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

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 stringstates. In the closed string sector, an integrable structure is inherited fromits parent theory, N=4 SYM. For the open string sector, the planar one-loopmixing matrix for gauge invariant holomorphic operators is identified with theHamiltonian of an integrable SU(3) open spin chain. Using the K-matrixformalism we identify the integrable open-chain boundary conditions thatcorrespond to string boundary conditions. The solutions to the algebraic Betheansatz equations (ABAE) with a few impurities are shown to recover theanomalous dimensions that exactly match the spectrum of free open string in theplane-wave background. We also discuss the properties of the solutions of ABAEbeyond the BMN regime.Comment: 18 pages, one eps figure, v3: typos corrected, clarifying footnotes added, treatment of complex roots revise