The Amplituhedron

Arkani-Hamed, Nima; Trnka, Jaroslav

doi:10.1007/jhep10(2014)030

Cited by 518 publications

(941 citation statements)

References 108 publications

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“…This analysis builds heavily on sections 3-5 of [3], and in particular we show how to recycle the one-loop boundaries classified there by "merging" pairs of one-loop boundaries into two-loop boundaries. We find that two different formulations of the amplituhedron -the original formulation in terms of C and D matrices [18], and the reformulation in terms of sign flips [19] -play two complementary roles, exactly as in [3]. Specifically, the former is useful for establishing the existence of boundaries by constructing explicit C and D matrix representatives, while the latter is useful for establishing the non-existence of any other boundaries.…”

Section: Classification Of Two-loop Boundariesmentioning

confidence: 95%

Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Prlina

Spradlin

Stankowicz

et al. 2018

J. High Energ. Phys.

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Abstract:In this sequel to [3] we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar N = 4 superYang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. We determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.

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Section: Classification Of Two-loop Boundariesmentioning

confidence: 95%

Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Prlina

Spradlin

Stankowicz

et al. 2018

J. High Energ. Phys.

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“…In this theory, a reformulation of perturbation theory exists in which tree and loop amplitudes are both directly represented in terms of on-shell diagrams, which can be computed as contour integrals over the (positive) Grassmannian G þ ðk; nÞ [7,8]. Moreover, the entire S matrix can be defined geometrically in terms of a space called the "amplituhedron" [9,10]. Unlike Feynman diagrams, on-shell diagrams do not represent local processes in space-time, but they make the Yangian symmetry of the theory completely manifest.…”

mentioning

confidence: 99%

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

Bourjaily²,

et al. 2014

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We present evidence that loop amplitudes in maximally supersymmetric (N ¼ 4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N ¼ 4 SYM has only logarithmic singularities and is free of any poles at infinity-properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N ¼ 8) supergravity theory (SUGRA).

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“…These variables manifest the dual symmetry, and trivialize both momentum conservation constraints and massless on-shell condition. Very recently, a direct dual formulation for all-loop amplitudes in momentum-twistor space, the "amplituhedron", was proposed [19] without explicitly referring to recursion relations or on-shell diagrams. In the amplituhedron, the planar integrand at any loop order is reformulated as forms in an auxiliary space.…”

Section: Jhep02(2015)065mentioning

confidence: 99%

“…Here we briefly review the definition of the amplituhedron [19]. At tree level, one can extract the super-amplitude from the "volume", or the form, of the tree amplituhedron.…”

Section: Jhep02(2015)065mentioning

confidence: 99%

The amplituhedron from momentum twistor diagrams

Bai

2015

J. High Energ. Phys.

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We propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N = 4 SYM, dubbed the "momentum-twistor diagrams". These are on-shell-diagrams obtained by gluing trivalent black and white vertices in momentum twistor space, which, in the reduced diagram case, are known to be related to diagrams in the original twistor space. The new diagrams are manifestly Yangian invariant, and they naturally represent factorization and forward-limit contributions in the all-loop BCFW recursion relations in momentum twistor space, in a fashion that is completely different from those in momentum space. We show how to construct and evaluate momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes and loop-level integrands; in particular the latter involve isolated bubble-structures for loop variables arising from forward limits, or the entangled removal of particles. From each diagram, the generalized "boundary measurement" directly gives the C, D matrices, thus a cell in the amplituhedron associated with the amplitude, and we expect that our diagrammatic representations of the amplitude provide triangulations of the amplituhedron. To demonstrate the computational power of the formalism, we give explicit results for general two-loop integrands, and the cells of the amplituhedron for two-loop MHV amplitudes.

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The Amplituhedron

Cited by 518 publications

References 108 publications

Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

The amplituhedron from momentum twistor diagrams

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