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

TL;DR

This paper demonstrates a simplified non-perturbative expression for Wilson line structure constants with 3 cusps in N=4 SYM using Quantum Spectral Curve, supporting its role in encoding correlation functions with all wrapping corrections.

Contribution

It provides a new simplified formula for structure constants with 3 cusps in the ladder limit using Q-functions, extending the Quantum Spectral Curve's application beyond anomalous dimensions.

Findings

Simplified non-perturbative expression for structure constants.

Evidence that Quantum Spectral Curve encodes all wrapping corrections.

Extension of results to scalar insertions and OPE expansion.

Abstract

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 results for the spectrum and the structure constants to this case. 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.