Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Yacine Ikhlef
  • Alexi Morin-Duchesne

Organisationseinheiten

Externe Organisationen

  • Sorbonne Université
  • Max-Planck-Institut für Mathematik
  • Universiteit Gent
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer030
Seitenumfang47
FachzeitschriftSciPost Physics
Jahrgang12
Ausgabenummer1
PublikationsstatusVeröffentlicht - 20 Jan. 2022

Abstract

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.

Zitieren

Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models. / Ikhlef, Yacine; Morin-Duchesne, Alexi.
in: SciPost Physics, Jahrgang 12, Nr. 1, 030, 20.01.2022.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Ikhlef Y, Morin-Duchesne A. Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models. SciPost Physics. 2022 Jan 20;12(1):030. doi: 10.21468/SciPostPhys.12.1.030
Ikhlef, Yacine ; Morin-Duchesne, Alexi. / Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models. in: SciPost Physics. 2022 ; Jahrgang 12, Nr. 1.
Download
@article{60dde7f6e23c4ad89008aaa356297a87,
title = "Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models",
abstract = "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. ",
keywords = "math-ph, cond-mat.stat-mech, hep-th, math.MP",
author = "Yacine Ikhlef and Alexi Morin-Duchesne",
note = "Publisher Copyright: {\textcopyright} The Author(s), 2021.",
year = "2022",
month = jan,
day = "20",
doi = "10.21468/SciPostPhys.12.1.030",
language = "English",
volume = "12",
number = "1",

}

Download

TY - JOUR

T1 - Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models

AU - Ikhlef, Yacine

AU - Morin-Duchesne, Alexi

N1 - Publisher Copyright: © The Author(s), 2021.

PY - 2022/1/20

Y1 - 2022/1/20

N2 - 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.

AB - 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.

KW - math-ph

KW - cond-mat.stat-mech

KW - hep-th

KW - math.MP

UR - http://www.scopus.com/inward/record.url?scp=85124402313&partnerID=8YFLogxK

U2 - 10.21468/SciPostPhys.12.1.030

DO - 10.21468/SciPostPhys.12.1.030

M3 - Article

VL - 12

JO - SciPost Physics

JF - SciPost Physics

IS - 1

M1 - 030

ER -