English

On invariants of Modular categories beyond modular data

Quantum Algebra 2018-07-02 v2 Strongly Correlated Electrons Quantum Physics

Abstract

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 WW-matrix--the quantum invariant of a colored framed Whitehead link from the associated TQFT of a modular category. We prove that the WW-matrix and the set of punctured SS-matrices are strictly beyond the modular data (S,T)(S,T). Whether or not the triple (S,T,W)(S,T,W) constitutes a complete invariant of modular categories remains an open question.

Keywords

Cite

@article{arxiv.1805.05736,
  title  = {On invariants of Modular categories beyond modular data},
  author = {Parsa Bonderson and Colleen Delaney and César Galindo and Eric C. Rowell and Alan Tran and Zhenghan Wang},
  journal= {arXiv preprint arXiv:1805.05736},
  year   = {2018}
}

Comments

24 pages; references to arXiv:1606.04378 and arXiv:1806.02843 are added

R2 v1 2026-06-23T01:55:43.659Z