Duality between Wilson loops and gluon amplitudes

Henn, Johannes M.

doi:10.1002/prop.200900048

Cited by 31 publications

(28 citation statements)

References 233 publications

(741 reference statements)

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“…It will be interesting to study the application of the ideas of on-shell recursion at loop level to maximally supersymmetric Yang-Mills theory in four dimensions as it opens a window to prove conjectured properties of the integrals and integrands such as dual conformal invariance and its one-loop breaking (see [49] and references therein and thereto).…”

Section: Discussionmentioning

confidence: 99%

On BCFW shifts of integrands and integrals

Boels

2010

J. High Energ. Phys.

116

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In this article a first step is made towards the extension of Britto-CachazoFeng-Witten (BCFW) tree level on-shell recursion relations to integrands and integrals of scattering amplitudes to arbitrary loop order. Surprisingly, it is shown that the large BCFW shift limit of the integrands has the same structure as the corresponding tree level amplitude in any minimally coupled Yang-Mills theory in four or more dimensions. This implies that these integrands can be reconstructed from a subset of their 'single cuts'. The main tool is powercounting Feynman graphs in a special lightcone gauge choice employed earlier at tree level by Arkani-Hamed and Kaplan. The relation between shifts of integrands and shifts of its integrals is investigated explicitly at one loop. Two particular sources of discrepancy between the integral and integrand are identified related to UV and IR divergences. This is cross-checked with known results for helicity equal amplitudes at one loop. The nature of the on-shell residue at each of the single-cut singularities of the integrand is commented upon. Several natural conjectures and opportunities for further research present themselves.

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Section: Discussionmentioning

confidence: 99%

On BCFW shifts of integrands and integrals

Boels

2010

J. High Energ. Phys.

116

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“…for the hexagonal light-like Wilson loop, which is dual to the six-gluon MHV amplitude [8,9] (for reviews see [26,27] and references therein, and [28,29] for recent developments). In [30], a remarkably simple form of the six-point remainder function [8,9] was given, based on previous work [31].…”

Section: Jhep04(2011)083mentioning

confidence: 99%

New differential equations for on-shell loop integrals

Drummond

Henn

Trnka

2011

J. High Energ. Phys.

155

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We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N = 4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N = 4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.

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“…In N " 4 supersymmetric Yang-Mills theory, the connection between scattering amplitudes and Wilson loops goes even further, cf. the reviews [59,60] for a more detailed discussion of the ideas sketched below. The first signs of the conjectured duality were observed by Alday and Maldacena [61], who found that maximally helicity violating (MHV) gluon scattering amplitudes at strong coupling are described by the area of certain minimal surfaces and hence identical to the Maldacena-Wilson loop over the respective boundary contour.…”

Section: Duality To Scattering Amplitudesmentioning

confidence: 99%

Wilson loops and integrability

Münkler¹

2020

J. Phys. A: Math. Theor.

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These notes provide an introduction toward Wilson loops in N " 4 supersymmetric Yang-Mills theory with a focus toward their integrability properties. In addition to a brief discussion of exact results for the circular Wilson loop and the cusp anomalous dimension, the notes focus on non-local symmetries, utilizing the integrability of the minimal surface problem that appears at strong coupling. This work is based on lectures given at the Young Researchers Integrability School and Workshop 2018. To appear in a special issue of J. Phys. A.

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Duality between Wilson loops and gluon amplitudes

Cited by 31 publications

References 233 publications

On BCFW shifts of integrands and integrals

On BCFW shifts of integrands and integrals

New differential equations for on-shell loop integrals

Wilson loops and integrability

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