Ground state degeneracy and module category

2023/11/01 by Ken Kikuchi, Kikuchi, Ken · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2311.00746

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 \lfloorFPdim(\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.

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