Year: 2023
Type: preprint
Abstract: We develop a systematic method to classify connected étale algebras $A$'s in (possibly degenerate) pre-modular category $\mathcal B$. In particular, we find the category of $A$-modules, $\mathcal B_A$, have ranks bounded from above by $\lfloor\text{FPdim}(\mathcal B)\rfloor$. For demonstration, we classify connected étale algebras in some $\mathcal B$'s, which appear in physics. Physically, the results constrain (or fix) ground state degeneracies of (certain) $\mathcal B$-symmetric gapped phases. We study massive deformations of rational conformal field theories such as minimal models and Wess-Zumino-Witten models. In most of our examples, the classification suggests the symmetries $\mathcal B$'s are spontaneously broken.
Source: arXiv (Cornell University)
Author: Kikuchi, Ken
Institution: National Taiwan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388328598