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Résumé |
We give a pedagogical introduction to the Quantum Spectral Curve of N=4 SYM
and discuss its applications to correlation functions. We find a massive
simplification in the non-perturbative expression for the
structure constant of Wilson lines with 3 cusps when expressed in terms of the
key Quantum Spectral Curve quantities, namely Q-functions. Our calculation is
done for the configuration of 3 cusps lying in the same plane with arbitrary
angles in the ladders limit. This provides strong evidence that the Quantum
Spectral Curve is not only a highly efficient tool for finding the anomalous
dimensions but also encodes correlation functions with all wrapping
corrections taken into account to all orders in the `t Hooft coupling. We also
show how to study the insertions of scalars coupled to the Wilson lines and
extend our result for the spectrum and the structure constant for these
states. We discuss an OPE expansion of two cusps in terms of these states. Our
results give additional support to the Separation of Variables strategy in
solving the planar N = 4 SYM theory. |
