Classification of Metaplectic Fusion Categories

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Eddy Ardonne
  • Peter E. Finch
  • Matthew Titsworth

Research Organisations

External Research Organisations

  • Stockholm University
  • University of Texas at Dallas
View graph of relations

Details

Original languageEnglish
Article number2102
JournalSymmetry
Volume13
Issue number11
Publication statusPublished - 5 Nov 2021

Abstract

In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for \(so(2p+1)_2\). These categories describe non-abelian anyons dubbed `metaplectic anyons'. We obtain explicit expressions for all the \(F\)- and \(R\)-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.

Keywords

    math.QA, Metaplectic anyons, Fusion category, Gauge invariants

ASJC Scopus subject areas

Cite this

Classification of Metaplectic Fusion Categories. / Ardonne, Eddy; Finch, Peter E.; Titsworth, Matthew.
In: Symmetry, Vol. 13, No. 11, 2102, 05.11.2021.

Research output: Contribution to journal › Article › Research › peer review

Ardonne, E, Finch, PE & Titsworth, M 2021, 'Classification of Metaplectic Fusion Categories', Symmetry, vol. 13, no. 11, 2102. https://doi.org/10.3390/sym13112102
Ardonne, E., Finch, P. E., & Titsworth, M. (2021). Classification of Metaplectic Fusion Categories. Symmetry, 13(11), Article 2102. https://doi.org/10.3390/sym13112102
Ardonne E, Finch PE, Titsworth M. Classification of Metaplectic Fusion Categories. Symmetry. 2021 Nov 5;13(11):2102. doi: 10.3390/sym13112102
Ardonne, Eddy ; Finch, Peter E. ; Titsworth, Matthew. / Classification of Metaplectic Fusion Categories. In: Symmetry. 2021 ; Vol. 13, No. 11.
Download
@article{cc47a9dbbe284539ab3ce461d311520b,
title = "Classification of Metaplectic Fusion Categories",
abstract = " In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for \(so(2p+1)_2\). These categories describe non-abelian anyons dubbed `metaplectic anyons'. We obtain explicit expressions for all the \(F\)- and \(R\)-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes. ",
keywords = "math.QA, Metaplectic anyons, Fusion category, Gauge invariants",
author = "Eddy Ardonne and Finch, {Peter E.} and Matthew Titsworth",
note = "Funding Information: Funding: E. Ardonne was supported, in part, by the Swedish research council, under Grant No. 2015-05043. P. E. Finch was supported by the Deutsche Forschungsgemeinschaft under Grant No. Fr 737/7-1.",
year = "2021",
month = nov,
day = "5",
doi = "10.3390/sym13112102",
language = "English",
volume = "13",
journal = "Symmetry",
issn = "2073-8994",
publisher = "Multidisciplinary Digital Publishing Institute",
number = "11",

}

Download

TY - JOUR

T1 - Classification of Metaplectic Fusion Categories

AU - Ardonne, Eddy

AU - Finch, Peter E.

AU - Titsworth, Matthew

N1 - Funding Information: Funding: E. Ardonne was supported, in part, by the Swedish research council, under Grant No. 2015-05043. P. E. Finch was supported by the Deutsche Forschungsgemeinschaft under Grant No. Fr 737/7-1.

PY - 2021/11/5

Y1 - 2021/11/5

N2 - In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for \(so(2p+1)_2\). These categories describe non-abelian anyons dubbed `metaplectic anyons'. We obtain explicit expressions for all the \(F\)- and \(R\)-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.

AB - In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for \(so(2p+1)_2\). These categories describe non-abelian anyons dubbed `metaplectic anyons'. We obtain explicit expressions for all the \(F\)- and \(R\)-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.

KW - math.QA

KW - Metaplectic anyons

KW - Fusion category

KW - Gauge invariants

UR - http://www.scopus.com/inward/record.url?scp=85118926563&partnerID=8YFLogxK

U2 - 10.3390/sym13112102

DO - 10.3390/sym13112102

M3 - Article

VL - 13

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 11

M1 - 2102

ER -