Algebraic structures in integrable field theories

该项目的目的是研究在可积场论中发现的代数结构，使用微扰代数量子场论的新框架。后者已经成功地应用于研究的sine-Gordon模型的一个项目主管（KR）。我们的想法是将这种方法应用到一个更大的类的可积场论，并调查它们之间的关系。代数结构，在这个更大的类的可积场论可以描述使用新的形式主义的二面角仿射Gaudin模型最近推出的一个项目主管（BV）。该项目的另一个方向将是连接二面角仿射高丁模型的形式主义与微扰代数量子场论。这将被用来研究经典场论和量子可积场论之间的某些约束对偶。

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.