Integrability in N=4 super Yang-Mills theory

We use the Bethe ansatz to calculate the cusp anomalous dimension in planar N=4 super Yang-Mills theory as an exact function of the coupling constant. The calculation allows us to fix the remaining ambiguities in the integrable system describing the spectrum of operators/string energy levels in the AdS/CFT correspondence.The cusp anomalous dimension is not affected by finite size effects, which in general remain ill-understood. We suggest a method for computing the lowest example of an anomalous dimension modified by such corrections.