The Baxter Q Operator of Critical Dense Polymers

Abstract

We consider critical dense polymers ${\mathcal{L}}_{1,2}$, corresponding to a logarithmic conformal field theory with central charge $c=-2$. An elegant decomposition of the Baxter $Q$ operator is obtained in terms of a finite number of lattice integrals of motion. All local, non local and dual non local involutive charges are introduced directly on the lattice and their continuum limit is found to agree with the expressions predicted by conformal field theory. A highly non trivial operator $\Psi (\nu )$ is introduced on the lattice taking values in the Temperley Lieb Algebra. This $\Psi$ function provides a lattice discretization of the analogous function introduced by Bazhanov, Lukyanov and Zamolodchikov. It is also observed how the eigenvalues of the $Q$ operator reproduce the well known spectral determinant for the harmonic oscillator in the continuum scaling limit.

improved version, accepted for publishing on JSTAT

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• Logarithmic extensions of minimal models: characters and modular transformations
• Associative-algebraic approach to logarithmic conformal field theories
• Solvable Critical Dense Polymers
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Cited by in corpus (3)

• Solvable Critical Dense Polymers on the Cylinder
• Modular invariant partition function of critical dense polymers
• Infinitely extended Kac table of solvable critical dense polymers