Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

By J. Drummond, J. Henn, G. Korchemsky, E. Sokatchev. 2007

437 citations recorded by the source corpus.

Planar gluon amplitudes in N=4N=4 SYM are remarkably similar to expectation values of Wilson loops made of light-like segments. We argue that the latter can be determined by making use of the conformal symmetry of the gauge theory, broken by cusp anomalies. We derive the corresponding anomalous conformal Ward identities valid to all loops and show that they uniquely fix the form of the finite part of a Wilson loop with n cusps (up to an additive constant) for n=4n=4 and 5 and reduce the freedom in it to a function of conformal invariants for n⩾6n⩾6. We also present an explicit two-loop calculation for n=5n=5. The result confirms the form predicted by the Ward identities and matches the finite part of the two-loop five-gluon planar MHV amplitude, up to a constant. This constitutes another non-trivial test of the Wilson loop/gluon amplitude duality.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b595ace62d6bad81260c5e6f4692f34f510b5637

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Citations in the corpus

Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, background): “For example, the dual conformal symmetry is expected to be broken in a way governed by an anomalous dual conformal Ward identity [33, 37].”
An operator product expansion for polygonal null Wilson loops (2010, background): “by the special conformal symmetry anomalous Ward identities [11].”
Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection (2008, background): “Of course one needs to treat IR divergences carefully (see [6]), but this is the essence of the statement.”
Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills (2011, result): “The slight mismatch here with boundary terms was to be fully expected: the naive Ward identities should be modified to account for the infrared divergences, probably in a very similar way to the bosonic case [41].”
Classical polylogarithms for amplitudes and Wilson loops. (2010, background): “[5] J.”
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “The duality with Wilson loops [3, 4, 5, 6, 7, 8, 9] and the associated dual conformal symmetry [7, 10, 11, 12, 13] of the planar theory mean that only amplitudes with six or more external legs are non-trivial.”
From correlation functions to scattering amplitudes (2010, background): “It was first proposed at strong coupling [2] and soon afterwards also observed at weak coupling, first at one loop [3, 4], followed by extensive two-loop tests [5, 6, 7, 8].”
Bootstrapping an NMHV amplitude through three loops (2014, background): “In addition, empirical results have led to the discovery of many hidden properties of planar N = 4 SYM, such as dual (super)conformal invariance [8–12], and the amplitude-Wilson-loop duality [11, 13–16].”
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “Understanding the role of this remarkable integrable structure in the full quantum theory, however, was clouded by the IR-divergences that appear to almost completely destroy the symmetry at loop-level, leaving only the anomalous action of the (Bosonic) dual conformal invariance [29–32].”
The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space (2010, background): “) Our proposal is motivated by the corresponding proposal in dual space-time that null polygonal Wilson loops yield the planar MHV amplitude to all loop orders [8, 9, 10, 11, 12, 13, 14, 15, 16].”
The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, neutral): “2) hWA(x 1,x 2,x 3,x 4)L(x 5)i hWA(x 1,x 2,x 3,x 4)i = 2 π2 x2 13x 2 24 x2 15 2 25 2 35 2 45 F(x) +O(ǫ) (2.6) It will serve us as the ﬁnite integrand mentioned above. It is possible to show following [35] that UV divergences cancel in the ratio of correlation functions on the left-hand side of (2.6)”
Single-valued harmonic polylogarithms and the multi-Regge limit (2012, background): “Rather, there is an anomaly, which was first understood in terms of polygonal Wilson loops rather than amplitudes [7].”