The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems

We explore the relationship between the SU(2) sector of a general integrable field theory and the all-loop guess for the anomalous dimensions of SU(2) operators in N = 4 super Yang-Mills theory. We demonstrate that the SU(2) structure of a nested Bethe ansatz alone reproduces much of the all-loop guess without depending on the details of the particular field theory. We speculate on the implications of this for strings in AdS5×S being described by the multi-particle states of an integrable worldsheet theory, and relate the techniques here to the known relationship between the Hubbard model and the all-loop guess.