Light-cone lattices and the exact solution of chiral fermion and sigma models

Abstract

A rich set of integrable two-dimensional quantum field theories are obtained from integrable lattice vertex models with q states per bound (q>or=2) in the scaling limit by a generalisation of the light-cone lattice approach. Chiral fermion models with any simple Lie group of symmetry arise in this way (for finite q) as well as bosonic models like the principal chiral model (for q= infinity ). The Hamiltonian, momentum and colour-conserved currents are constructed on the lattice and the bare equations of motion are derived. The renormalised mass spectrum is given explicitly for the set of models considered here. All these integrable vertex models yield conformal invariant theories if one takes the scalding limit in an appropriate different way. It is argued that the values one obtains for the central charges are the same as those provided by the Sugawara construction (in the continuum) for all simple Lie algebras.