Physical theories that do not involve dimensionful couplings are usually symmetric, at the classical level, under the inversion transformation of space-time coordinates x -> 1/x that relates small and large distances. The conventional Lorentz (Poincare) transformations complemented by inversion form together a larger symmetry group, called conformal group. This symmetry in Quantum Chromodynamcs (QCD) is broken by quantum corrections, but its "imprints" remain in the form of nontrivial constraints on the structure of the short-distance expansion and the renormalization group equations.

We study the constraints imposed by conformal symmetry on the structure of evolution equations and power-suppressed contributions to hard exclusive reactions involving a large momentum transfer, e.g., for the deeply-virtual Compton scattering.

Source: Jahrbuch 2011 des Alumnivereins der Fakultät für Physik

der Universität Regensburg

It has been found that certain QCD evolution equations possess an additional, "hidden" symmetry that is not seen at the Lagrangian level: they are mathematically equivalent to completely integrable spin chain models. This symmetry allows one to obtain exact analytic solutions using a powerful mathematical approach known as Quantum Inverse Scattering Method.

A review and some of our recent publications can be found here.