Systematics of the cusp anomalous dimension

Abstract

We study the velocity-dependent cusp anomalous dimension in supersymmetric Yang-Mills theory. In a paper by Correa, Maldacena, Sever, and one of the present authors, a scaling limit was identified in which the ladder diagrams are dominant and are mapped onto a Schrodinger problem. We show how to solve the latter in perturbation theory and provide an algorithm to compute the solution at any loop order. The answer is written in terms of harmonic polylogarithms. Moreover, we give evidence for two curious properties of the result. Firstly, we observe that the result can be written using a subset of harmonic polylogarithms only, at least up to six loops. Secondly, we show that in a light-like limit, only single zeta values appear in the asymptotic expansion, again up to six loops. We then extend the analysis of the scaling limit to systematically include subleading terms. This leads to a Schrodinger-type equation, but with an inhomogeneous term. We show how its solution can be computed in perturbation theory, in a way similar to the leading order case. Finally, we analyze the strong coupling limit of these subleading contributions and compare them to the string theory answer. We find agreement between the two calculations.

33 pages, 4 figures. Complete LO six-loop result added. Typos corrected. Version accepted for publication

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• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Single-valued harmonic polylogarithms and the multi-Regge limit
• The cusp anomalous dimension at three loops and beyond
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Cusped SYM Wilson loop at two loops and beyond
• Multiple zeta values and periods of moduli spaces ${\mathfrak{M}}_{0,n}$
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• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle
• Quark--anti-quark potential in N=4 SYM
• Exact Bremsstrahlung and Effective Couplings
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• From Webs to Polylogarithms
• Multiple Gluon Exchange Webs
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• An Introduction to Webs
• Integral representations combining ladders and crossed-ladders
• A factorization approach to next-to-leading-power threshold logarithms
• Ladder Limit for Correlators of Wilson Loops
• Position-space cuts for Wilson line correlators
• Cusped Wilson lines in symmetric representations
• NLL resummation for the static potential in N=4 SYM theory
• Notes on BPS Wilson Loops and the Cusp Anomalous Dimension in ABJM theory
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• Non-equilibrium Wilson loops in N=4 SYM
• On the cusp anomalous dimension in the ladder limit of $\mathcal{N}=4$ SYM
• Progress on soft gluon exponentiation and long-distance singularities
• Boomerang webs up to three-loop order