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

@article{Bern2005IterationOP, title={Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond}, author={Zvi Bern and Lance J. Dixon and Vladimir A. Smirnov}, journal={Physical Review D}, year={2005}, volume={72}, pages={085001} }

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 finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is…

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## References

SHOWING 1-10 OF 140 REFERENCES

### 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.

### Three-loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model

- Physics
- 2004

### Two point functions of chiral operators in N=4 SYM at order g**4

- Mathematics
- 1999

We compute two-point functions of chiral operators Tr Φ3 in = 4 SU(N) supersymmetric Yang-Mills theory to the order g4 in perturbation theory. We perform explicit calculations using = 1 superspace…