Fast QSC Solver: tool for systematic study of N=4 Super-Yang-Mills spectrum
arXiv (Cornell University)(2023)
摘要
Integrability methods give us access to a number of observables in the planar
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 Δ_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
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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关键词
fast qsc solver,spectrum,super-yang-mills
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