Work

Tropical geometry, quantum affine algebras, and scattering amplitudes

Year: 2024

Type: article

Abstract: The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas: (1) We give a systematic construction of prime modules (including prime non-real modules) of quantum affine algebras using tropical geometry. We also introduce new objects which generalize positive tropical Grassmannians. (2) We propose a generalization of Grassmannian string integrals in physics, in which the integrand is a product indexed by prime modules of a quantum affine algebra. We give a general formula of u-variables using prime tableaux (corresponding to prime modules of quantum affine algebras of type A) and Auslander–Reiten quivers of Grassmannian cluster categories. (3) We study limit g-vectors of cluster algebras. This is another way to obtain prime non-real modules of quantum affine algebras systematically. Using limit g-vectors, we construct new examples of non-real modules of quantum affine algebras.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ad909b

Authors: Nick Early, Jian-Rong Li

Institutions: Institute for Advanced Study, University of Vienna

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165

Funders: Deutsche Forschungsgemeinschaft, Austrian Science Fund, European Research Council, H2020 European Research Council