W-extended logarithmic minimal models

Rasmussen, Jorgen (2009) W-extended logarithmic minimal models. Nuclear Physics B, 807 3: 495-533. doi:10.1016/j.nuclphysb.2008.07.029

Author Rasmussen, Jorgen
Title W-extended logarithmic minimal models
Formatted title
W-extended logarithmic minimal models
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
Publication date 2009-02
Sub-type Article (original research)
DOI 10.1016/j.nuclphysb.2008.07.029
Open Access Status DOI
Volume 807
Issue 3
Start page 495
End page 533
Total pages 39
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Formatted abstract
We consider the continuum scaling limit of the infinite series of Yang–Baxter integrable logarithmic minimal models LM(p,p′) as ‘rational’ logarithmic conformal field theories with extended W symmetry. The representation content is found to consist of 6pp′−2p−2pW-indecomposable representations of which 2p+2p′−2 are of rank 1, 4pp′−2p−2p′ are of rank 2, while the remaining 2(p−1)(p′−1) are of rank 3. We identify these representations with suitable limits of Yang–Baxter integrable boundary conditions on the lattice. The W-indecomposable rank-1 representations are all W-irreducible while we present a conjecture for the embedding patterns of the W-indecomposable rank-2 and -3 representations. The associated W-extended characters are all given explicitly and decompose as finite non-negative sums of W-irreducible characters. The latter correspond to W-irreducible subfactors and we find that there are 2pp′+(p−1)(p′−1)/2 of them. We present fermionic character expressions for some of the rank-2 and all of the rank-3 W-indecomposable representations. To distinguish between inequivalent W-indecomposable representations of identical characters, we introduce ‘refined’ characters carrying information also about the Jordan-cell content of a representation. Using a lattice implementation of fusion on a strip, we study the fusion rules for the W-indecomposable representations and find that they generate a closed fusion algebra, albeit one without identity for p>1. We present the complete set of fusion rules and interpret the closure of this fusion algebra as confirmation of the proposed extended symmetry. Finally, 2pp′ of the W-indecomposable representations are in fact W-projective representations and they generate a closed fusion subalgebra.
Keyword Conformal field theory
Algebraic approach
Fusion algebras
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 23 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 23 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Wed, 14 Mar 2012, 12:37:58 EST by Kay Mackie on behalf of Mathematics