# Amplitudes and correlators to ten loops using simple, graphical bootstraps

@article{Bourjaily2016AmplitudesAC, title={Amplitudes and correlators to ten loops using simple, graphical bootstraps}, author={Jacob L. Bourjaily and Pauline Heslop and Vuong-Viet Tran}, journal={Journal of High Energy Physics}, year={2016}, volume={2016}, pages={1-32} }

A bstractWe introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their…

## 54 Citations

Perturbative correlation functions and scattering amplitudes in planar N=4 supersymmetric Yang-Mills

- Mathematics
- 2018

In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric N=4 Yang-Mills.
We…

Perturbative Correlation Functions and Scattering Amplitudes in Planar $\mathcal{N}=4$ Supersymmetric Yang-Mills

- Mathematics
- 2018

In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric N = 4 Yang-Mills. We use…

Bootstrapping the Simplest Correlator in Planar N=4 Supersymmetric Yang-Mills Theory to All Loops.

- PhysicsPhysical review letters
- 2020

We present the full form of a four-point correlation function of large BPS operators in planar N=4 supersymmetric Yang-Mills theory to any loop order. We do this by following a bootstrap philosophy…

Multi-particle amplitudes from the four-point correlator in planar N = 4 SYM

- Mathematics
- 2018

A non-trivial consequence of the super-correlator/super-amplitude duality is that the integrand of the four-point correlation function of stress-tensor multiplets in planar N = 4 super Yang-Mills…

Amplitudes at Infinity

- Physics
- 2018

We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric quantum field theories in four dimensions. We check residue-theorem identities…

Deep Into the Amplituhedron: Amplitude Singularities at All Loops and Legs.

- PhysicsPhysical review letters
- 2019

A canonical set of cuts of the integrand for maximally helicity violating amplitudes in planar N=4 supersymmetric Yang-Mills theory, where all internal propagators are put on shell is computed.

Perturbative Four-Point Functions In Planar N = 4 SYM From Hexagonalization

- Mathematics
- 2018

We use hexagonalization to compute four-point correlation functions of long BPS operators with special R-charge polarizations. We perform the computation at weak coupling and show that at any loop…

All five-loop planar four-point functions of half-BPS operators in N=4$$ \mathcal{N}=4 $$ SYM

- MathematicsJournal of High Energy Physics
- 2018

A bstractWe obtain all planar four-point correlators of half-BPS operators in N=4$$ \mathcal{N}=4 $$ SYM up to five loops. The ansatz for the integrand is fixed partially by imposing lightcone OPE…

MITP / 18-077 UUITP-34 / 18 TCDMATH 1809 All five-loop planar four-point functions of half-BPS operators in N = 4 SYM

- Mathematics
- 2018

We obtain all planar four-point correlators of half-BPS operators in N = 4 SYM up to five loops. The ansatz for the integrand is fixed partially by imposing lightcone OPE relations between different…

Prescriptive unitarity for non-planar six-particle amplitudes at two loops

- MathematicsJournal of High Energy Physics
- 2019

Abstract
We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes…

## References

SHOWING 1-10 OF 64 REFERENCES

From correlation functions to scattering amplitudes

- Mathematics
- 2010

A bstractWe study the correlation functions of half-BPS protected operators in $ \mathcal{N} = {4} $ super-Yang-Mills theory, in the limit where the positions of adjacent operators become light-like…

Local integrand representations of all two-loop amplitudes in planar SYM

- Mathematics
- 2015

A bstractWe use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally…

Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

- Physics
- 2013

A bstractIntegrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate…

Notes on the scattering amplitude — Wilson loop duality

- Mathematics
- 2011

We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We…

Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

- Mathematics
- 2007

We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence…

Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond

- Physics
- 2005

We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the…

Planar amplitudes in maximally supersymmetric Yang-Mills theory.

- PhysicsPhysical review letters
- 2003

This work demonstrates that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes and conjecture an analogous relation for n-point amplitudes.