Classification of connected \'etale algebras in modular fusion categories up to rank five

Autor:	Kikuchi, Ken
Rok vydání:	2023
Předmět:	Mathematics - Quantum Algebra Condensed Matter - Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Mathematics - Category Theory
Druh dokumentu:	Working Paper
Popis:	We classify connected \'etale algebras in (possibly non-unitary) modular fusion categories $\mathcal B$'s with $\text{rank}(\mathcal B)\le5$. We also comment on Lagrangian algebra, anyon condensation, and physical applications. Concretely, we prove certain spontaneous $\mathcal B$-symmetry breaking and predict ground state degeneracies in massive renormalization group flows from non-unitary minimal models. Comment: 32 pages + references; v2: minor corrections on Toric Code, fixed typos; v3: minor corrections on $psu(2)_9$, and added a theorem in section 3.1 proving modular fusion categories $\mathcal B$'s with $\text{rank}(\mathcal B)>1$ are spontaneously broken; v4: minor corrections on $\text{Vec}_{\mathbb Z/2\mathbb Z\times\mathbb Z/2\mathbb Z}$; v5:corrected method and typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.13353 Zobrazit plný text záznamu View this record from Arxiv