Work

Quantum affine algebras, cluster algebras, and their connections with scattering amplitudes

Year: 2026

Type: article

Abstract: Quantum affine algebras are a fundamental family of infinite-dimensional quantum groups with profound connections to integrable systems, solvable lattice models, and conformal and quantum field theories. In recent years, scattering amplitudes in gauge theory, particularly in planar N = 4 supersymmetric Yang–Mills theory, quantum chromodynamics, and related models, have revealed unexpected mathematical structures, including cluster algebras from Grassmannians and partial flag varieties. Meanwhile, the Grothendieck rings of finite-dimensional representations of quantum affine algebras have been shown to carry canonical cluster algebra structures closely related to those arising from Grassmannians and partial flag varieties. These connections open a pathway for transferring methods and results from the theory of quantum affine algebras to the study of scattering amplitudes. In this survey, we review recent developments in this emerging interface, highlighting the representation-theoretic and cluster-algebraic structures that play an increasingly important role in the modern study of scattering amplitudes.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ae79bb

Author: Jian-Rong Li

Institution: 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: $3,325

Funder: National Natural Science Foundation of China