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Related papers: Symbol Alphabets from Plabic Graphs

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We exploit the recently described property of cluster adjacency for scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory to construct the symbol of the four-loop NMHV heptagon amplitude. We use a manifestly cluster…

High Energy Physics - Theory · Physics 2020-04-16 James Drummond , Jack Foster , Ömer Gürdoğan , Georgios Papathanasiou

Motivated by reformulating Yangian invariants in planar ${\cal N}=4$ SYM directly as $d\log$ forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the $d\log$'s, which we call "letters", for…

High Energy Physics - Theory · Physics 2021-03-17 Song He , Zhenjie Li

We revisit the conjectural method called Schubert analysis for generating the alphabet of symbol letters for Feynman integrals, which was based on geometries of intersecting lines associated with corresponding cut diagrams. We explain the…

High Energy Physics - Theory · Physics 2024-10-16 Song He , Xuhang Jiang , Jiahao Liu , Qinglin Yang

By breaking dual conformal invariance, we transform cluster-algebraic predictions for the alphabet of 9-point amplitudes in $\mathcal{N}=4$ super Yang-Mills theory to analogous predictions for 5- and 6-point processes in QCD. We start by…

High Energy Physics - Theory · Physics 2026-03-18 Rigers Aliaj , Garbriele Dian , Georgios Papathanasiou

Gaetz, Pechenik, Pfannerer, Striker, and Swanson introduced the concept of hourglass plabic graphs and provided a method for computing web diagrams and invariants corresponding to $4\times n$ Young tableaux, while Elkin, Musiker, and Wright…

Combinatorics · Mathematics 2025-07-25 Wen Ting Zhang , Rui Zhi Tang , Jin Xing Zhao

We study Feynman integrals and scattering amplitudes in ${\cal N}=4$ super-Yang-Mills by exploiting the duality with null polygonal Wilson loops. Certain Feynman integrals, including one-loop and two-loop chiral pentagons, are given by…

High Energy Physics - Theory · Physics 2021-06-16 Song He , Zhenjie Li , Qinglin Yang , Chi Zhang

We show how Supersymmetric Ward identities can be used to obtain amplitudes involving gluinos or adjoint scalars from purely gluonic amplitudes. We obtain results for all one-loop six-point NMHV amplitudes in $\NeqFour$ Super Yang-Mills…

High Energy Physics - Theory · Physics 2009-11-11 Steven J. Bidder , David C. Dunbar , Warren B. Perkins

We study cluster adjacency conjectures for amplitudes in maximally supersymmetric Yang-Mills theory. We show that the n-point one-loop NMHV ratio function satisfies Steinmann cluster adjacency. We also show that the one-loop BDS-like…

High Energy Physics - Theory · Physics 2021-02-03 Jorge Mago , Anders Schreiber , Marcus Spradlin , Anastasia Volovich

We derive analytic results for the symbol of certain two-loop Feynman integrals relevant for seven- and eight-point two-loop scattering amplitudes in planar $\mathcal{N}=4$ super-Yang--Mills theory. We use a bootstrap inspired strategy,…

High Energy Physics - Theory · Physics 2018-11-14 Johannes Henn , Enrico Herrmann , Julio Parra-Martinez

Seven-point amplitudes in planar ${\cal N}=4$ super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual…

High Energy Physics - Theory · Physics 2020-10-28 Lance J. Dixon , Yu-Ting Liu

We review the bootstrap method for constructing six- and seven-particle amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, by exploiting their analytic structure. We focus on two recently discovered properties which greatly…

We study a scalar component of the 8-point next-to-next-to-maximally-helicity-violating (N${}^2$MHV) amplitude at two-loop level in ${\cal N}=4$ super-Yang-Mills theory; it has a leading singularity proportional to the inverse of the…

High Energy Physics - Theory · Physics 2023-01-18 Song He , Zhenjie Li , Chi Zhang

We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of…

High Energy Physics - Theory · Physics 2017-08-02 Tristan Dennen , Igor Prlina , Marcus Spradlin , Stefan Stanojevic , Anastasia Volovich

We define recursion relations for N = 8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar N = 4 super-Yang-Mills. Although the recursion relations generically give rise to non-planar on-shell…

High Energy Physics - Theory · Physics 2016-06-29 Paul Heslop , Arthur E. Lipstein

We compute the symbol of the two-loop five-point scattering amplitude in $\mathcal{N}$ = 4 super-Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless…

High Energy Physics - Theory · Physics 2019-04-03 Samuel Abreu , Lance J. Dixon , Enrico Herrmann , Ben Page , Mao Zeng

We propose that the symbol alphabet for classes of planar, dual-conformal-invariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of)…

High Energy Physics - Theory · Physics 2022-01-05 Song He , Zhenjie Li , Qinglin Yang

We review an algorithm for determining the branch points of general amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory from amplituhedra. We demonstrate how to use the recent reformulation of amplituhedra in terms of `sign flips'…

High Energy Physics - Theory · Physics 2018-07-04 Igor Prlina , Marcus Spradlin , James Stankowicz , Stefan Stanojevic , Anastasia Volovich

I present a conjecture that all two-loop MHV amplitudes in planar $\mathcal{N} = 4$ super-Yang-Mills theory possess an antipodal symmetry when evaluated on parity-even kinematics. The symmetry acts as a change of basis on the symbol…

High Energy Physics - Theory · Physics 2022-09-28 Yu-Ting Liu

In this note we further investigate the procedure for computing tree-level amplitudes in Yang-Mills theory from connected instantons in the B-model on P^{3|4}, emphasizing that the problem of calculating Feynman diagrams is recast into the…

High Energy Physics - Theory · Physics 2011-05-05 Radu Roiban , Marcus Spradlin , Anastasia Volovich

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols…

High Energy Physics - Theory · Physics 2015-11-11 James M. Drummond , Georgios Papathanasiou , Marcus Spradlin