Infinitely extended Kac table of solvable critical dense polymers

Pearce, Paul A., Rasmussen, Jørgen and Villani, Simon P. (2013) Infinitely extended Kac table of solvable critical dense polymers. Journal of Physics A - Mathematical and Theoretical, 46 17: 1-38. doi:10.1088/1751-8113/46/17/175202

Author Pearce, Paul A.
Rasmussen, Jørgen
Villani, Simon P.
Title Infinitely extended Kac table of solvable critical dense polymers
Journal name Journal of Physics A - Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
Publication date 2013-05
Sub-type Article (original research)
DOI 10.1088/1751-8113/46/17/175202
Volume 46
Issue 17
Start page 1
End page 38
Total pages 38
Place of publication United Kingdom
Publisher Institute of Physics Publishing
Collection year 2014
Language eng
Formatted abstract
Solvable critical dense polymers is a Yang–Baxter integrable model of polymers on the square lattice. It is the first member ℒℳ(1,2) of the family of logarithmic minimal models ℒℳ(p,p'). The associated logarithmic conformal field theory admits an infinite family of Kac representations labelled by the Kac labels r, s = 1, 2, .... In this paper, we explicitly construct the conjugate boundary conditions on the strip. The boundary operators are labelled by the Kac fusion labels (r, s) = (r, 1) ⊗ (1, s) and involve a boundary field ξ. Tuning the field ξ appropriately, we solve exactly for the transfer matrix eigenvalues on arbitrary finite-width strips and obtain the conformal spectra using the Euler–Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double-row transfer matrices. The transfer matrix eigenvalues are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields selection rules for the physically relevant solutions to the inversion identity which takes the form of a decomposition into irreducible blocks corresponding combinatorially to finitized characters given by generalized q-Catalan polynomials. This decomposition is in accord with the decomposition of the Kac characters into irreducible characters. In the scaling limit, we confirm the central charge c = −2 and the Kac formula for the conformal weights Δr,s= {(2r-s)²-1} / 8 for r, s = 1, 2, 3, ... in the infinitely extended Kac table.
Keyword Logarithmic minimal models
Conformal field-theories
A-face models
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article 175202.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
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Citation counts: TR Web of Science Citation Count  Cited 8 times in Thomson Reuters Web of Science Article | Citations
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