Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models
Yacine Ikhlef, Alexi Morin-Duchesne
SciPost Phys. 12, 030 (2022) · published 20 January 2022
- doi: 10.21468/SciPostPhys.12.1.030
In two-dimensional loop models, the scaling properties of critical random curves are encoded in the correlators of connectivity operators. In the dense O($n$) loop model, any such operator is naturally associated to a standard module of the periodic Temperley-Lieb algebra. We introduce a new family of representations of this algebra, with connectivity states that have two marked points, and argue that they define the fusion of two standard modules. We obtain their decomposition on the standard modules for generic values of the parameters, which in turn yields the structure of the operator product expansion of connectivity operators.
Cited by 1
Grans-Samuelsson et al., Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
SciPost Phys. 12, 147 (2022) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Yacine Ikhlef,
- 2 3 4 Alexi Morin-Duchesne