HET-Discovery seminar: Fedor Levkovich-Maslyuk

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. This provides evidence that the Quantum Spectral Curve is not only a highly efficient tool for finding the anomalous dimensions but also encodes exact correlation functions. We also show how to study the insertions of scalars coupled to the Wilson lines and extend to them our result for the spectrum and the structure constants. 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.