Counting paths with Schur transitions

Díaz, Pablo ; Kemp, Garreth ; Véliz-Osorio, Alvaro

Resumen: In this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which is valid for any rank of the unitary group, reproduces known asymptotic results. We proceed to establish the general validity of this expression by a formal proof. The form of this equation strongly hints towards a quantum generalization. Thus, we introduce a notion of quantum relative dimension and subject it to the appropriate consistency tests. This new quantity finds its natural environment in the context of RCFTs and fractional statistics; where the already established notion of quantum dimension has proven to be of great physical importance.

Idioma: Inglés

DOI: 10.1016/j.nuclphysb.2016.08.008

Año: 2016

Publicado en: NUCLEAR PHYSICS B 911 (2016), 295-317
ISSN: 0550-3213

Factor impacto JCR: 3.678 (2016)

Categ. JCR: PHYSICS, PARTICLES & FIELDS rank: 10 / 29 = 0.345 (2016) - Q2 - T2

Factor impacto SCIMAGO: 2.21 - Nuclear and High Energy Physics (Q1)

Tipo y forma: Artículo (Versión definitiva)