Abstract
Integrability methods give us access to a number of observables in the planar \( \mathcal{N} \) = 4 SYM. Among them, the Quantum Spectral Curve (QSC) governs the spectrum of anomalous dimensions. Low lying states were successfully studied in the past using the QSC. However, with the increased demand for a systematic study of a large number of states for various applications, there is a clear need for a fast 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 219 states with the bare dimension ∆0 ≤ 6 in a wide range of couplings.
The new algorithm has an improved performance at weak coupling and allows to glue numerics smoothly the available perturbative data, resolving the previous obstruction. Further ∼ 8-fold efficiency gain comes from C++ implementation over the best available Mathematica implementation. We have made the code and the data to be available via a GitHub repository.
The method is generalisable for non-local observables as well as for other theories such as deformations of \( \mathcal{N} \) = 4 SYM and ABJM. It may find applications in the separation of variables and bootstrability approaches to the correlation functions. Some applications to correlators at strong coupling are also presented.
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Acknowledgments
We are very grateful to Luis Fernando Alday, Tobias Hansen and Joao Silva for stimulating discussions, and for sharing some of their unpublished work with us. We thank Dionysios Anninos, Andrea Cavaglià, Jeremy Mann, Sameer Murthy, Michelangelo Preti and Dmytro Volin for discussions related to some parts of this work. We thank Andrea Cavaglià for beta testing the GitHub repository. The work of Á.H. was supported by the NKFIH grant K134946. The work of N.G., J.J. and N.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 865075) EXACTC. The work of N.G. was also partially supported by the STFC grant (ST/P000258/1).
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Gromov, N., Hegedűs, Á., Julius, J. et al. Fast QSC solver: tool for systematic study of \( \mathcal{N} \) = 4 Super-Yang-Mills spectrum. J. High Energ. Phys. 2024, 185 (2024). https://doi.org/10.1007/JHEP05(2024)185
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DOI: https://doi.org/10.1007/JHEP05(2024)185