Harmony of super form factors

Brandhuber, Andreas; Gürdoğan, Ömer; Mooney, Robert; Travaglini, Gabriele; Yang, Gang

doi:10.1007/jhep10(2011)046

Cited by 96 publications

(215 citation statements)

References 83 publications

(183 reference statements)

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“…Generalized unitarity can also be applied to objects containing local gauge-invariant operators such as correlation functions [5] and form factors [6,7,[26][27][28][29][30][31][32][33][34][35][36]. Since generalized unitarity is a momentum space method, the local operators will have to be Fourier transformed.…”

Section: Generalized Unitaritymentioning

confidence: 99%

“…The form factors for these operators are very simple as the operators respect part of the supersymmetry. They have been dealt with extensively in the papers [7,34]. For our purposes we are only going to need MHV form factors as we will explain later.…”

Section: Jhep02(2016)030mentioning

confidence: 99%

“…If x i and y1 are light-like separated the integral will not influence the subsequent integrals and one can do the same analysis for the second right-most integral. 7 This argument suggests that integrals of the type in (4.21) satisfy the relation:…”

Section: Scalar Polygonmentioning

confidence: 99%

“…Similarly, the diagram only contributes to 7 The observant reader will notice that one could also make y1 light-like separated from both xi and xi+1 and not worry about the remaining Lagrangian insertions. When including the spinor structure of the on-shell Lagrangian the special three-point kinematics makes the spinors λ α for the three sides of the light-like triangle proportional to each other.…”

Section: Scalar Polygonmentioning

confidence: 99%

“…Finally the result is Fourier transformed back into position space [5]. This approach has many merits: form factors of some operators have been shown to have simple structures reminiscent of the ones found in scattering amplitudes [6,7], and, although the work cited here deals with N = 4 super-Yang-Mills, it could easily be applied to other theories. Unfortunately, correlation functions are best expressed in position space so some of the symmetries may not be apparent until after the Fourier transform.…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian insertion in the light-like limit and the super-correlators/super-amplitudes duality

Engelund

2016

J. High Energ. Phys.

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In these notes we describe how to formulate the Lagrangian insertion technique in a way that mimics generalized unitarity. We introduce a notion of cuts in position space and show that the cuts of the correlators in the super-correlators/super-amplitudes duality correspond to generalized unitarity cuts of the equivalent amplitudes. The cuts consist of correlation functions of operators in the chiral part of the stress-tensor multiplet as well as other half-BPS operators. We will also discuss the application of the method to other correlators as well as non-planar contributions.

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Section: Generalized Unitaritymentioning

confidence: 99%

Section: Jhep02(2016)030mentioning

confidence: 99%

Section: Scalar Polygonmentioning

confidence: 99%

Section: Scalar Polygonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lagrangian insertion in the light-like limit and the super-correlators/super-amplitudes duality

Engelund

2016

J. High Energ. Phys.

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On-Shell Techniques for Tree-Level Amplitudes

Badger,

Henn,

Plefka

et al. 2024

Lecture Notes in Physics

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In this chapter we focus on the pole structure of tree-level amplitudes. We argue that amplitudes factorise on these poles into lower-point amplitudes. Moreover, universal factorisation structures emerge when two momenta become collinear as well as in the limit of low energy of a single particle—the soft limit. These factorisation properties are the basis of an efficient technique for computing tree-level scattering amplitudes in gauge theories and gravity recursively—without ever referring to Feynman rules or even a Lagrangian. These recursion relations use as input lower-point amplitudes, so that the gauge redundancy, which is partly responsible for the complexity of conventional Feynman graph calculations, is absent in this entirely on-shell based formalism. We then show the invariance of scattering amplitudes under Poincaré transformations, and introduce the conformal symmetry of gauge-theory tree-level amplitudes. Finally, we highlight a surprising double-copy relation between gluon and graviton amplitudes.

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Wilson Loop Form Factors: A New Duality

Chicherin¹,

Heslop²,

Korchemsky³

et al. 2018

Springer Proceedings in Mathematics &Amp; Statistics

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We find a new duality for form factors of lightlike Wilson loops in planar N = 4 super-Yang-Mills theory. The duality maps a form factor involving an n-sided lightlike polygonal super-Wilson loop together with m external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analytic continuation from Minkowski to Euclidean space. We illustrate all of these subtleties explicitly in the simplest non-trivial NMHV-like case. and the identification of coordinates with momenta (1.3) to their supersymmetric analogs. The super-Wilson loop form factors are considered in the planar limit and in the lowestorder perturbative approximation (Born level). The introduction of Grassmann variables (θ i on the Wilson loop contour and η j for the on-shell states) allows us to probe the duality for more complicated configurations of particle helicities. By analogy with the amplitudes, we call the contributions at the lowest level in the Grassmann expansion MHV-like, at the next level NMHV-like, etc. At MHV level we confirm the result of [20]. The NMHV level is much more complicated, the form factor being a non-trivial rational function of the kinematical data. Yet, we show that the duality still works, in a rather simple and suggestive way, by just matching planar Feynman diagrams. This allows us to argue that it should hold for the complete supersymmetric object (at all Grassmann levels) and also beyond the Born approximation.The key to understanding the duality is the appropriate superspace formulation of the Wilson loop and its form factor. In the conventional approach the chiral supersymmetric Wilson loop [4,5,6] is formulated in terms of constrained on-shell super-connections [21,22], which makes the Feynman diagram technique highly inefficient. In this paper we prefer to use the Lorentz harmonic chiral (LHC) superspace approach [23]. It provides an offshell formulation of the chiral N = 4 SYM theory in terms of unconstrained prepotentials, best suited for supersymmetric quantisation. LHC superspace is an alternative to the twistor formulation [24,25], closer in spirit to traditional field theory (see also [26]). The main idea is to consider the interacting theory as a perturbation of the self-dual sector. The twistor formulation has been successfully used to justify the so-called MHV rules for the computation of the amplitude [27], to prove the duality between supersymmetric Wilson loops and amplitudes [5], to compute off-shell correlation functions of the N = 4 stress-tensor multiplet [28]. More recently, the LHC formalism was applied to finding the non-chiral completion of the correlators [29] and to the calculation of form facto...

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Harmony of super form factors

Cited by 96 publications

References 83 publications

Lagrangian insertion in the light-like limit and the super-correlators/super-amplitudes duality

Lagrangian insertion in the light-like limit and the super-correlators/super-amplitudes duality

On-Shell Techniques for Tree-Level Amplitudes

Wilson Loop Form Factors: A New Duality

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