Algebraic structures in integrable field theories

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The aim of the project is to study algebraic structures discovered in integrable field theories, using the novel framework of perturbative algebraic quantum field theory. The latter has already been successfully applied in the study of the sine-Gordon model by one of the project supervisors (KR). The idea is to apply this approach to a larger class of integrable field theories and to investigate relationships between them.Algebraic structures in this larger class of integrable field theories can be described using the novel formalism of dihedral affine Gaudin models recently introduced by one of the project supervisors (BV). Another direction of the project will be to connect the formalism of dihedral affine Gaudin models with that of perturbative algebraic quantum field theory. This will be used to investigate certain conjectured dualities between classical and quantum integrable field theories.