The full spectrum of AdS 5 /CFT 4 II: Weak coupling expansion via the quantum spectral curve

We continue the effort to optimise and generalise the solution of the spectral problem of AdS 5 /CFT 4 in the planar limit via integrability. We present a simple strategy to solve the quantum spectral curve (QSC) perturbatively for general states by focussing on the P μ -system. A Mathematica notebook with an implementation of this algorithm is provided, as well as an extensive database with a user-friendly interface containing more than 8000 solutions of the QSC. When investigating the solution space, we observe a curious phenomenon: existence of solutions for which the Q-system degenerates in the limit g → 0. These degeneracies are lifted at higher orders in perturbation theory. The degenerating solutions have auxiliary Bethe roots merging with branch points at weak coupling.