Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

Details Integrals of Motion for Critical Dense Polymers and Symplectic Fermions Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

2009-03-29

arxiv.org/abs/0903.5051v4

J. Stat. Mech. (2009) P10007

Physics

High Energy Physics

High Energy Physics - Theory

53 pages, version accepted for publishing on JSTAT

Scientific paper

We consider critical dense polymers ${\cal L}(1,2)$. 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.

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