N=4 super-Yang-Mills theory and integrable spin chains

We show that for any (integrable) spin chain with nearest neighbor interactions there exists at least one field theory such that the generator of scale transformations can be represented, on some operators, by the Hamiltonian of the spin chain. We identify an anisotropic spin chain corresponding to the q-deformation of N = 4 super-Yang Mills theory and diagonalize it using the algebraic Bethe ansatz. We briefly discuss some of the implications of the integrable spin chains describing the dilatation operators of various sectors of various field theories to the calculations of some correlation functions of gauge invariant operators.