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arXiv · 1711.10053

Quantum deformation of planar amplitudes

Michael Movshev·Albert Schwarz
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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 $q$-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.

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Michael Movshev, Albert Schwarz. 2017-11-28. Quantum deformation of planar amplitudes. https://doi.org/10.1007/jhep04(2018)121

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