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Grassmannian integral for general gauge invariant off-shell amplitudes in \( \mathcal{N}=4 \) SYM

  • L.V. BorkEmail author
  • A.I. Onishchenko
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in \( \mathcal{N}=4 \) SYM with arbitrary number of off-shell gluons or equivalently Wilson line operator insertions. We make a conjecture for the Grassmannian integral representation for such objects and verify our conjecture on several examples. It is remarkable that in our formulation one can consider situation when on-shell particles are not present at all, i.e. we have Grassmannian integral representation for purely off-shell object. In addition we show that off-shell amplitude with arbitrary number of off-shell gluons could be also obtained using quantum inverse scattering method for auxiliary \( \mathfrak{g}\mathfrak{l}\left(4\Big|4\right) \) super spin chain.

Keywords

Scattering Amplitudes Supersymmetric Gauge Theory Integrable Field Theories Extended Supersymmetry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.The Center for Fundamental and Applied ResearchAll-Russia Research Institute of AutomaticsMoscowRussia
  3. 3.Bogoliubov Laboratory of Theoretical PhysicsJointInstitute for Nuclear ResearchDubnaRussia
  4. 4.Moscow Institute of Physics and TechnologyState UniversityDolgoprudnyRussia
  5. 5.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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