We present a new formalism, alternative to the old thermodynamic-Bethe-ansatz-like approach, for solution of the spectral problem of planar $\mathcal{N}=4$ super Yang-Mills theory. It takes a concise form of a nonlinear matrix Riemann-Hilbert problem in terms of a few $Q$ functions. We demonstrate the formalism for two types of observables—local operators at weak coupling and cusped Wilson lines in a near Bogomol’nyi-Prasad-Sommerfield limit.

• Received 31 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.011602