Fast QSC Solver: tool for systematic study of N=4 Super-Yang-Mills spectrum

Integrability methods give us access to a number of observables in the planarN=4 SYM. Among them, the Quantum Spectral Curve (QSC) governs the spectrum ofanomalous dimensions. Low lying states were successfully studied in the pastusing the QSC. However, with the increased demand for a systematic study of alarge number of states for various applications, there is a clear need for afast QSC solver which can easily access a large number of excited states. Here,we fill this gap by developing a new algorithm and applied it to study all 219states with the bare dimension $\Delta_0 \leq 6$ in a wide range of couplings.The new algorithm has an improved performance at weak coupling and allows toglue numerics smoothly the available perturbative data, resolving the previousobstruction. Further ~ 8-fold efficiency gain comes from C++ implementationover the best available Mathematica implementation. We have made the code andthe data to be available via a GitHub repository. The method is generalisablefor non-local observables as well as for other theories such as deformations ofN=4 SYM and ABJM. It may find applications in the separation of variables andbootstrability approaches to the correlation functions. Some applications tocorrelators at strong coupling are also presented.