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

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.

31 pages, 1 figure; v2: minor correctons

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• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
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• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
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• Progress and prospects of lattice supersymmetry
• A review of the AdS/CFT Quantum Spectral Curve
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• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
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• Wilson Loops and Integrability
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
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