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arXiv · 2311.02353

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

Tadashi Udagawa
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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.

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Tadashi Udagawa. 2023-11-04. Solutions of the tt*-equations constructed from the SU(2)$_k$-fusion ring, and Smyth potentials. https://arxiv.org/abs/2311.02353

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