Open Fishchain in N=4 Supersymmetric Yang-Mills Theory

TL;DR

This paper demonstrates the integrability of a specific Wilson line configuration in N=4 SYM, modeling it as an open boundary quantum fishchain, and derives the spectrum non-perturbatively.

Contribution

It introduces the open boundary quantum fishchain model for a cusped Wilson line in N=4 SYM and derives the Baxter equation and spectrum quantization.

Findings

Proves all-loop integrability of the model.

Derives the Baxter equation for the system.

Numerically computes the non-perturbative spectrum.

Abstract

We consider a cusped Wilson line with J insertions of scalar fields in N=4 SYM and prove that in a certain limit the Feynman graphs are integrable to all loop orders. We identify the integrable system as a quantum fishchain with open boundary conditions. The existence of the boundary degrees of freedom results in the boundary reflection operator acting non-trivially on the physical space. We derive the Baxter equation for Q-functions and provide the quantisation condition for the spectrum. This allows us to find the non-perturbative spectrum numerically.