Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

TL;DR

This paper analyzes critical dense polymers using the Thermodynamic Bethe Ansatz to derive eigenvalues of local integrals of motion, revealing their relation to symplectic fermions and lattice structures.

Contribution

It introduces a method to compute lattice integrals of motion for dense polymers and relates them to continuum conformal field theory and symplectic fermions.

Findings

Eigenvalues of integrals of motion are obtained via TBA.

Transfer matrix decomposes into finite lattice integrals of motion.

Lattice integrals of motion relate to continuum integrals as infinite sums.

Abstract

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.