Scaling limits of integrable quantum field theories (Q2891036)

Modern theory of non-perturbative renormalization is at the core of many achievements of contemporary physics. Historically, the renormalization group technique had its origin in scale invariance. The requirement that scattering amplitudes are independent of our choice of the energy scale at which the theory is renormalized lead to the Callan-Symanzik equation from 1970. The most important application of computing the large energy limit is the asymptotic freedom of quantum chromodynamics. In the present article the authors study the scaling limit of a class of integrable models in 1+1-dimensional space-time. It is interesting to note that two-dimensional sigma models share with QCD the property of asymptotic freedom. There exist many different approaches to obtaining scaling limits. Within the context of algebraic quantum field theory, Buchholz and Verch reconsidered the renormalization group and introduced so-called scaling algebras. One can also make use of so-called wedge-local quantum field, i.e. fields that are localized in infinite wedge-shaped space-time regions. The algebraic as well as the wedge technique is used in the present article. It is shown that limit theories exist for integrable field theories. They disintegrate into tensor products of chiral field theories covariant under translations. Consider now observables that are localized in finite light ray intervals. On the subspace generated by applying these observables to the vacuum, this dilation symmetry can be extended to the Möbius group, i.e. the scaling limit extends to a conformal quantum field on the circle.