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Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six

Ken Kikuchi, Kah-Sen Kam, Fu-Hsiang Huang

Abstract

We classify connected étale algebras $A$'s in multiplicity-free modular fusion categories (MFCs) $\mathcal{B}$'s at rank six, namely $\text{rank}(\mathcal{B})=6$. There are eight MFCs in total and the result indicates that only $so(5)_2$ has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right $A$-modules in $so(5)_2$. Finally, we discuss physical applications, specifically proving spontaneous $\mathcal{B}$-symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models.

Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six

Abstract

We classify connected étale algebras 's in multiplicity-free modular fusion categories (MFCs) 's at rank six, namely . There are eight MFCs in total and the result indicates that only has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right -modules in . Finally, we discuss physical applications, specifically proving spontaneous -symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models.
Paper Structure (18 sections, 112 equations, 9 tables)

This paper contains 18 sections, 112 equations, 9 tables.

Table of Contents

  1. Introduction
  2. Classification
  3. Definitions
  4. Method
  5. Classification
  6. $\mathcal{B}\simeq\text{Vec} _{\mathbb Z/6\mathbb Z}^\alpha$
  7. $\mathcal{B}\simeq\text{Vec}_{\mathbb Z/2\mathbb Z}^{-1}\boxtimes\text{Ising}$
  8. $\mathcal{B}\simeq su(3)_2\simeq\text{Fib}\boxtimes\text{Vec}_{\mathbb Z/3\mathbb Z}^1$
  9. $\mathcal{B}\simeq\text{TriCritIsing}$
  10. $\mathcal{B}\simeq su(2)_5\simeq\text{Vec}_{\mathbb Z/2\mathbb Z}^{-1}\boxtimes psu(2)_5$
  11. $\mathcal{B}\simeq so(5)_2$
  12. $\mathcal{B}\simeq\text{Fib}\boxtimes psu(2)_5$
  13. $\mathcal{B}\simeq psu(2)_{11}$
  14. Physical applications
  15. Theorems
  16. ...and 3 more sections