Quark--anti-quark potential in N=4 SYM

TL;DR

This paper develops a comprehensive method using the Quantum Spectral Curve to calculate the quark--anti-quark potential in N=4 SYM at any coupling, providing high-precision numerical results and analytical weak coupling expansions.

Contribution

It introduces a novel asymptotic approach within the Quantum Spectral Curve framework for calculating the potential at all couplings in planar N=4 SYM.

Findings

Accurate numerical solutions matching string theory predictions.

First seven terms of weak coupling expansion analytically computed.

Reduced the problem to a Schrödinger equation in a specific limit.

Abstract

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion. Moreover, we study analytically the generalized quark--anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.