Title: Solutions of the tt*-equations constructed from the SU(2)$_k$-fusion ring, and Smyth potentials Show Chinese title

Title: 从 SU(2)$_k$-融合环构造的 tt*-方程的解，以及 Smyth 势

Abstract: Cecotti and Vafa introduced the tt*-equation (topological-antitopological fusion equation), whose solutions describe massive deformations of supersymmetric conformal field theories. We describe some solutions of the tt*-equation constructed from the SU(2)$_k$-fusion algebra. The idea of the construction is due to Cecotti and Vafa, but we give a precise mathematical formulation and a description of the "holomorphic data" corresponding to the solutions by using the DPW method. Furthermore, we give a relation between the solutions and the representations of SU(2). As a special case, we consider the solutions corresponding to the supersymmetric A$_k$-minimal model. Show Chinese abstract

Abstract: 塞科蒂和瓦法引入了tt*方程（拓扑-反拓扑融合方程），其解描述了超对称共形场论的大质量形变。 我们描述了一些由SU(2)$_k$-融合代数构造的tt*方程的解。 构造的思想归功于塞科蒂和瓦法，但我们通过DPW方法给出了一个精确的数学表述以及对应解的“全纯数据”的描述。 此外，我们给出了解与SU(2)表示之间的联系。 作为一个特例，我们考虑了与超对称A$_k$-最小模型相对应的解。