### Abstract

The form factor program for the regularized space–time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of ‘t Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space–time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion–antifermion pairs accounted for in NMHV two-channel conformal blocks.

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

Pages (from-to) | 113-136 |

Number of pages | 24 |

Journal | Nuclear Physics B |

Volume | 929 |

DOIs | |

State | Published - Apr 1 2018 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*929*, 113-136. https://doi.org/10.1016/j.nuclphysb.2018.01.031

**Resummed tree heptagon.** / Belitsky, Andrei.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 929, pp. 113-136. https://doi.org/10.1016/j.nuclphysb.2018.01.031

}

TY - JOUR

T1 - Resummed tree heptagon

AU - Belitsky, Andrei

PY - 2018/4/1

Y1 - 2018/4/1

N2 - The form factor program for the regularized space–time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of ‘t Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space–time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion–antifermion pairs accounted for in NMHV two-channel conformal blocks.

AB - The form factor program for the regularized space–time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of ‘t Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space–time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion–antifermion pairs accounted for in NMHV two-channel conformal blocks.

UR - http://www.scopus.com/inward/record.url?scp=85044528447&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044528447&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2018.01.031

DO - 10.1016/j.nuclphysb.2018.01.031

M3 - Article

AN - SCOPUS:85044528447

VL - 929

SP - 113

EP - 136

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -