Yang-Baxter symmetry in integrable models: new light from the Bethe ansatz solution

Abstract

We show how any integrable 2D QFT enjoys the existence of infinitely many non-abelian conserved charges satisfying a Yang-Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a representation of q-deformed affine Lie algebras. We review and generalize the work of de Vega, Eichenherr and Maillet on the bootstrap construction of the quantum monodromy operators to the sine-Gordon (or massive Thirring) model, where such operators do not possess a classical analogue. Within the light-cone approach to the mT model, we explicitly compute the eigenvalues of the six-vertex alternating transfer matrix τ(λ) on a generic physical state, through the algebraic Bethe ansatz. In the thermodynamic limit τ(λ) turns out to be a two-valued periodic function. One determination generates the local abelian charges, including energy and momentum, while the other yields the abelian subalgebra of the (non-local) YB algebra. In particular, the boostrap results coincide with the ratio between the two determinations of the lattice transfer matrix.