# The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

@article{Bern2007TheFP,
title={The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory},
author={Zvi Bern and Michal Czakon and Lance J. Dixon and David A. Kosower and Vladimir A. Smirnov},
journal={Physical Review D},
year={2007},
volume={75},
pages={085010}
}
• Published 23 October 2006
• Physics
• Physical Review D
We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and…
424 Citations

## Figures and Tables from this paper

### The four-loop cusp anomalous dimension in $\mathcal{N}$ = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals

• Mathematics
• 2013
A bstractCorrelation functions of Wilson lines are relevant for describing the infrared structure of scattering amplitudes. We develop a new method for evaluating a wide class of such Wilson line

### The four-loop cusp anomalous dimension in N = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals

• Physics
• 2013
Correlation functions of Wilson lines are relevant for describing the infrared structure of scattering amplitudes. We develop a new method for evaluating a wide class of such Wilson line integrals,

### Four-loop cusp anomalous dimension from obstructions

• Physics
• 2007
We introduce a method for extracting the cusp anomalous dimension at L loops from four-gluon amplitudes in N=4 Yang-Mills without evaluating any integrals that depend on the kinematical invariants.

### The three-loop form factor in $\mathcal{N} = {4}$ super Yang-Mills

• Mathematics
• 2011
A bstractIn this paper we study the Sudakov form factor in $\mathcal{N} = {4}$ super Yang-Mills theory to the three-loop order. The latter is expressed in terms of planar and non-planar loop

### Higgs-regularized three-loop four-gluon amplitude in $\mathcal{N} = 4$ SYM: exponentiation and Regge limits

• Mathematics
• 2010
We compute the three-loop contribution to the $\mathcal{N} = 4$ supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and

### Analytic result for the two-loop six-point NMHV amplitude in $\mathcal{N} = {4}$ super Yang-Mills theory

• Mathematics
• 2012
A bstractWe provide a simple analytic formula for the two-loop six-point ratio function of planar $\mathcal{N} = {4}$ super Yang-Mills theory. This result extends the analytic knowledge of

### Five-point amplitudes in N=4 super-Yang-Mills theory and N=8 supergravity

• Physics
• 2012
We present the complete integrands of five-point superamplitudes in N = 4 super-Yang-Mills theory and N = 8 supergravity, at one and two loops, for four-dimensional external states and D-dimensional

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

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

### One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry

• Physics
• 2009
We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is

## References

SHOWING 1-10 OF 70 REFERENCES

### Phys

• Lett. B 595, 521
• 2004

### Nucl

• Phys. B 664, 131
• 2003

### Phys

• Lett. B 557, 114
• 2003

### Phys

• Lett. B 401, 273
• 1997

### Phys

• Rev. D 72, 085001
• 2005

### Phys

• Rev. D 69, 046002
• 2004

### Phys

• Rev. D 42, 4222
• 1990

### Nucl

• Phys. B 636, 99
• 2002

### Phys

• Rev. Lett. 91, 251602
• 2003