# One-loop derivation of the Wilson polygon–MHV amplitude duality

@article{Gorsky2009OneloopDO, title={One-loop derivation of the Wilson polygon–MHV amplitude duality}, author={A. S. Gorsky and Alexander Zhiboedov}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2009}, volume={42}, pages={355214} }

We discuss the origin of the Wilson polygon–MHV amplitude duality at a perturbative level. It is shown that the duality for the MHV amplitudes at the one-loop level can be proven upon a particular change of variables in Feynman parametrization and with the use of the relation between Feynman integrals at different space-time dimensions. Some generalization of the duality which implies the insertion of a particular vertex operator at the Wilson triangle is found for the 3-point function. We…

## 15 Citations

### From correlation functions to Wilson loops

- Mathematics
- 2011

We start with an n−point correlation function in a conformal gauge theory. We show that a special limit produces a polygonal Wilson loop with n sides. The limit takes the n points towards the…

### Amplitudes at weak coupling as polytopes in AdS5

- Mathematics
- 2011

We show that one-loop scalar box functions can be interpreted as volumes of geodesic tetrahedra embedded in a copy of AdS5 that has dual conformal spacetime as boundary. When the tetrahedron is…

### Amplitudes in N = 4 SYM from the Quantum geometry of the Momentum Space

- Physics
- 2009

We discuss multiloop MHV amplitudes in the N = 4 SYM theory in terms of eﬀective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external…

### Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture

- Mathematics
- 2009

The present study illuminates the relation between null cusped Wilson loops and their corresponding amplitudes. We find that, compared to the case with no self-crossing, the one loop expectation…

### 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.

### PUPT-2319 CONSTRUCTION OF INFRARED FINITE OBSERVABLES IN N = 4 SUPER YANG-MILLS THEORY

- Mathematics
- 2009

In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for N = 4…

### Construction of infrared finite observables in N = 4 super Yang-Mills theory

- Mathematics
- 2010

In this paper we give all the details of the calculation that we presented in our previous paper [58], where the infrared structure of the maximally helicity violating gluon amplitudes in the planar…

### Amplitudes in the N=4 supersymmetric Yang-Mills theory from quantum geometry of momentum space

- Physics
- 2009

We discuss multiloop maximally helicity violating amplitudes in the N=4 supersymmetric Yang-Mills theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of…

## References

SHOWING 1-10 OF 53 REFERENCES

### Planar scattering amplitudes from Wilson loops

- Physics
- 2008

We derive an expression for parton scattering amplitudes of planar gauge theory in terms of sums of Wilson loops. We study in detail the example of Yang-Mills theory with an adjoint Higgs field. The…

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

- Physics
- 2010

### Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling

- Mathematics
- 2009

In this note we consider minimal surfaces in three dimensional anti-de Sitter space that end at the AdS boundary on a polygon given by a sequence of null segments. The problem can be reduced to a…

### Singularities and Discontinuities of Feynman Amplitudes

- Physics, Mathematics
- 1960

The Landau singularities of the amplitude calculated from an arbitrary Feynman graph are considered. It is shown that the discontinuity across a branch cut starting from any Landau singularity is…

### Implementation of the duality between Wilson loops and scattering amplitudes in QCD.

- PhysicsPhysical review letters
- 2009

It is shown that the area-law behavior of asymptotically large Wilson loops is dual to the Regge-Veneziano behavior of scattering amplitudes at high energies and fixed momentum transfer, when the quark mass is small and/or the number of particles is large.

### On collinear factorization of Wilson loops and MHV amplitudes in = 4 SYM

- Mathematics
- 2008

We consider the (multi) Splitting function of Wilson loops and MHV gluon scattering S matrix elements in = 4 SYM. At strong coupling, one can utilize the methods of Alday and Maldacena and at weak…

### 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…