Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

Abstract

We consider critical dense polymers $\mathcal{L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.

53 pages, version accepted for publishing on JSTAT

References in corpus (9)

• Logarithmic Minimal Models
• Logarithmic extensions of minimal models: characters and modular transformations
• Solvable Critical Dense Polymers
• Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model
• Fusion Algebras of Logarithmic Minimal Models
• The logarithmic triplet theory with boundary
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• On the Integrable Structure of the Ising Model

Cited by in corpus (9)

• The tensor structure on the representation category of the ${\mathcal{W}}_p$ triplet algebra
• Solvable Critical Dense Polymers on the Cylinder
• Modular invariant partition function of critical dense polymers
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Finite-size corrections for logarithmic representations in critical dense polymers
• W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
• Lattice Integrals of Motion of the Ising Model on the Cylinder
• Infinitely extended Kac table of solvable critical dense polymers
• Free Field realization of the ${\hat{\mathcal{D}}}_q$ Algebra for the $\eta$-$\xi$ system, Integrals of Motion and Characters