On invariants of Modular categories beyond modular data Article Swipe

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Modular design Invariant (physics) Mathematics Modular curve Modular invariance Pure mathematics Computer science Algebra over a field Programming language Mathematical physics

Parsa Bonderson , Colleen Delaney , César Galíndo , Eric C. Rowell , Alan Tran , Zhenghan Wang ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1805.05736 · OA: W2804919478

We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the $W$-matrix--the quantum invariant of a colored framed Whitehead link from the associated TQFT of a modular category. We prove that the $W$-matrix and the set of punctured $S$-matrices are strictly beyond the modular data $(S,T)$. Whether or not the triple $(S,T,W)$ constitutes a complete invariant of modular categories remains an open question.