Logarithmic minimal models

By P. Pearce, J. Rasmussen, Jean-Bernard Zuber. 2006

193 citations recorded by the source corpus.

Working in the dense loop representation, we use the planar Temperley–Lieb algebra to build integrable lattice models called logarithmic minimal models . Specifically, we construct Yang–Baxter integrable Temperley–Lieb models on the strip acting on link states and consider their associated Hamiltonian limits. These models and their associated representations of the Temperley–Lieb algebra are inherently non-local and not (time-reversal) symmetric. We argue that, in the continuum scaling limit, they yield logarithmic conformal field theories with central charges c = 1−(6(p−p′)2/pp′), where p, p′ = 1, 2, ... are coprime. The first few members of the principal series are critical dense polymers (m = 1, c = −2), critical percolation (m = 2, c = 0) and the logarithmic Ising model (m = 3, c = 1/2). For the principal series, we find an infinite family of integrable and conformal boundary conditions organized in an extended Kac table with conformal weights Δr,s = (((m+1)r−ms)2−1)/4m(m+1), r, s = 1, 2, .... The associated conformal partition functions are given in terms of Virasoro characters of highest-weight representations. Individually, these characters decompose into a finite number of characters of irreducible representations. We show with examples how indecomposable representations arise from fusion.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1e22b814ac4c30ec379a1b37fb2f4a8e05de1907

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Yi-Zhi Huang
2. Lin Zhang
3. James Lepowsky
4. Haisheng Li
5. C. Dong

In Discrete Mathematics and Combinatorics

1. Yi-Zhi Huang
2. Lin Zhang
3. James Lepowsky

In Geometry and Topology

1. T. Creutzig
2. David Ridout
3. James Lepowsky
4. Lin Zhang
5. H. Saleur
6. N. Read
7. Yi-Zhi Huang
8. Jinwei Yang

Citations in the corpus

• Associative-algebraic approach to logarithmic conformal field theories (2007, background): “Box 208120,New Haven,CT 06520-8120 USA b Service de Physique Th eorique,CEA Saclay, G ifSurYvette,91191,France c D epartm entofPhysicsand Astronom y,University ofSouthern California LosAngeles,CA 90089,USA”
• Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and their Generalized Modules (2010, methodology): “tex operator superalgebras (see [AM3], [AM5] and [AM7]). Results have also been obtained for the vertex operator subalgebras of the algebras W(p,q) generated by the Virasoro algebra (see [GK2], [EF], [PRZ], [ReS], [MR], [RP1], [BFGT] and [GV]). The C 2-cofiniteness of the W(2,q)-algebras has been pro”
• Logarithmic conformal field theory: beyond an introduction (2013, background): “In particular, we work almost entirely in the continuum, expecting that the reader is familiar with rational conformal field theory as described (for example) in [14], eschewing approaches based on statistical lattice models and conjectured scaling limits (see [15–18]).”