### Abstract

We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N=4 super-Yang-Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.

Original language | English (US) |
---|---|

Pages (from-to) | 108-135 |

Number of pages | 28 |

Journal | Nuclear Physics B |

Volume | 894 |

DOIs | |

State | Published - May 1 2015 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Fermionic pentagons and NMHV hexagon.** / Belitsky, Andrei.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 894, pp. 108-135. https://doi.org/10.1016/j.nuclphysb.2015.02.025

}

TY - JOUR

T1 - Fermionic pentagons and NMHV hexagon

AU - Belitsky, Andrei

PY - 2015/5/1

Y1 - 2015/5/1

N2 - We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N=4 super-Yang-Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.

AB - We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N=4 super-Yang-Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.

UR - http://www.scopus.com/inward/record.url?scp=84924663708&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924663708&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2015.02.025

DO - 10.1016/j.nuclphysb.2015.02.025

M3 - Article

AN - SCOPUS:84924663708

VL - 894

SP - 108

EP - 135

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -