Quantum deformation of planar amplitudes
High Energy Physics - Theory
2018-05-23 v2 Mathematical Physics
math.MP
Quantum Algebra
Abstract
In maximally supersymmetric four-dimensional gauge theories planar on-shell diagrams are closely related to the positive Grassmannian and the cell decomposition of it into the union of so called positroid cells \cite{A}. We establish that volume forms on positroids used to express scattering amplitudes can be -deformed to Hochschild homology classes of corresponding quantum algebras. The planar amplitudes are represented in \cite {A} as sums of contributions of some set of positroid cells; we quantize these contributions. In classical limit our considerations allow us to obtain explicit formulas for contributions of positroid cells to scattering amplitudes.
Cite
@article{arxiv.1711.10053,
title = {Quantum deformation of planar amplitudes},
author = {Michael Movshev and Albert Schwarz},
journal= {arXiv preprint arXiv:1711.10053},
year = {2018}
}