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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.
In Carqueville et al., arXiv:1809.01483, the notion of an orbifold datum $mathbb{A}$ in a modular fusion category $mathcal{C}$ was introduced as part of a generalised orbifold construction for Reshetikhin-Turaev TQFTs. In this paper, given a simple o
We study odd-dimensional modular tensor categories and maximally non-self dual (MNSD) modular tensor categories of low rank. We give lower bounds for the ranks of modular tensor categories in terms of the rank of the adjoint subcategory and the order
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category symmetrie
We use zesting and symmetry gauging of modular tensor categories to analyze some previously unrealized modular data obtained by Grossman and Izumi. In one case we find all realizations and in the other we determine the form of possible realizations;
The definitions of the $n^{th}$ Gauss sum and the associated $n^{th}$ central charge are introduced for premodular categories $mathcal{C}$ and $ninmathbb{Z}$. We first derive an expression of the $n^{th}$ Gauss sum of a modular category $mathcal{C}$,