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 mathcal{N}=4 SYM theory.
Highlights
Integrability is a unique tool allowing one to obtain exact non-perturbative results in fully interacting field theories even when the supersymmetry is of no use
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 a highly efficient tool for finding the anomalous dimensions and encodes correlation functions with all wrapping corrections taken into account to all orders in the ‘t Hooft coupling
Summary
Integrability is a unique tool allowing one to obtain exact non-perturbative results in fully interacting field theories even when the supersymmetry is of no use. The Q-functions are known to play the role of the wave functions in the Separation of Variables (SoV) program initiated for quantum integrable models in [16,17,18,19] and recently generalized to SU(N ) spin chains in [20] leading to a new algebraic construction for the states (see [21, 22]). We propose that it corresponds to one of the excited states in the Schrodinger equation (and to a well-defined analytic continuation in the QSC outside the ladders limit) We verified this claim at weak coupling by comparing with the direct perturbation theory calculation of [54].6. The appendices contain various technical details, in particular the detailed strong coupling expansion for the spectrum
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