# Cluster Adjacency Properties of Scattering Amplitudes in N=4 Supersymmetric Yang-Mills Theory.

@article{Drummond2018ClusterAP, title={Cluster Adjacency Properties of Scattering Amplitudes in N=4 Supersymmetric Yang-Mills Theory.}, author={James Drummond and Jack Foster and {\"O}mer G{\"u}rdoğan}, journal={Physical review letters}, year={2018}, volume={120 16}, pages={ 161601 } }

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

## 71 Citations

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- Mathematics
- 2020

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…

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- PhysicsProceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)
- 2020

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- MathematicsJournal of High Energy Physics
- 2021

Abstract
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N
= 4 super Yang-Mills theory. We argue…

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- MathematicsJournal of High Energy Physics
- 2021

Abstract
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- Mathematics
- 2020

We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory. In particular we conjecture that, given a maximal…

### All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories.

- MathematicsPhysical review letters
- 2018

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- 2022

: As part of the Snowmass community planning exercise, we highlight an ongoing program of research into the structure of scattering amplitudes in N = 4 super-Yang-Mills theory, particularly in the…

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- 2019

We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr( k, n ). A finite cluster algebra provides a…

### A note on one-loop cluster adjacency in N $$ \mathcal{N} $$ = 4 SYM

- Mathematics
- 2021

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…

### Folding Amplitudes into Form Factors: An Antipodal Duality.

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- 2022

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar N=4 super-Yang-Mills theory is dual to the six-gluon MHV amplitude on its parity-preserving…

## References

SHOWING 1-10 OF 25 REFERENCES

### Bootstrapping a Five-Loop Amplitude Using Steinmann Relations.

- PhysicsPhysical review letters
- 2016

It is shown that Steinmann relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory, and is obtained the complete five-loop six-particle amplitude.

### Cluster polylogarithms for scattering amplitudes

- Mathematics
- 2014

Motivated by the cluster structure of two-loop scattering amplitudes in N = 4 ?> Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight four are made…

### Classical polylogarithms for amplitudes and Wilson loops.

- MathematicsPhysical review letters
- 2010

A compact analytic formula is presented for the two-loop six-particle maximally helicity violating remainder function in N=4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Lik with cross ratios of momentum twistor invariants as their arguments.

### Gluon scattering amplitudes at strong coupling

- Physics
- 2007

We describe how to compute planar gluon scattering amplitudes at strong coupling in = 4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical…

### N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution

- Physics
- 2010

We further investigate, in the planar limit of N=4 supersymmetric Yang–Mills theories, the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut…

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

- Physics
- 2010

### Motivic amplitudes and cluster coordinates

- Mathematics
- 2014

A bstractIn this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free…

### Local integrals for planar scattering amplitudes

- Mathematics
- 2012

A bstractRecently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in $ \mathcal{N} = {4} $ SYM has been described, generalizing the BCFW formula for tree…