$a\times b=c$ in $2+1$D TQFT

Matthew Buican; Linfeng Li; Rajath Radhakrishnan

doi:10.22331/q-2021-06-04-468

$a\times b=c$ in $2+1$D TQFT

Matthew Buican, Linfeng Li, and Rajath Radhakrishnan

CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK

Published:	2021-06-04, volume 5, page 468
Eprint:	arXiv:2012.14689v4
Doi:	https://doi.org/10.22331/q-2021-06-04-468
Citation:	Quantum 5, 468 (2021).

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Abstract

We study the implications of the anyon fusion equation $a\times b=c$ on global properties of $2+1$D topological quantum field theories (TQFTs). Here $a$ and $b$ are anyons that fuse together to give a unique anyon, $c$. As is well known, when at least one of $a$ and $b$ is abelian, such equations describe aspects of the one-form symmetry of the theory. When $a$ and $b$ are non-abelian, the most obvious way such fusions arise is when a TQFT can be resolved into a product of TQFTs with trivial mutual braiding, and $a$ and $b$ lie in separate factors. More generally, we argue that the appearance of such fusions for non-abelian $a$ and $b$ can also be an indication of zero-form symmetries in a TQFT, of what we term "quasi-zero-form symmetries" (as in the case of discrete gauge theories based on the largest Mathieu group, $M_{24}$), or of the existence of non-modular fusion subcategories. We study these ideas in a variety of TQFT settings from (twisted and untwisted) discrete gauge theories to Chern-Simons theories based on continuous gauge groups and related cosets. Along the way, we prove various useful theorems.

► BibTeX data

@article{Buican2021timesbcindtqft,
  doi = {10.22331/q-2021-06-04-468},
  url = {https://doi.org/10.22331/q-2021-06-04-468},
  title = {{$a\times b=c$} in {$2+1$}D {TQFT}},
  author = {Buican, Matthew and Li, Linfeng and Radhakrishnan, Rajath},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {468},
  month = jun,
  year = {2021}
}

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[2] Matthew Buican and Rajath Radhakrishnan, "Galois orbits of TQFTs: symmetries and unitarity", Journal of High Energy Physics 2022 1, 4 (2022).

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