We construct the most general perturbatively long-range integrable spin chain with spins transforming in the fundamental representation of gl(N) and open boundary conditions. In addition to the previously determined bulk moduli we find a new set of p
arameters determining the reflection phase shift. We also consider finite-size contributions and comment on their determination.
In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symme
try algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.
We compute the dilatation generator in the su(2) sector of planar N=4 super Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed di
rectly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to zeta(3).
