*
Nikolay Gromov (King's Coll.London, Dept.Math & St.Petersburg, INP)
*

**
**

**
Quantum Spectral Curve and Structure Constants in N = 4 SYM: Cusps in the Ladder Limit
**

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.