The use of critical conformal invariance in renormalization of twist-2 operators

Abstract

This thesis explores the application of methods of Conformal Field Theory (CFT) in Quantum Field Theories where the classical conformal symmetry is broken. The main example and motivation for such studies is Quantum Chromodynamics (QCD), but other theories are discussed as well. In particular, we focus on the problem of the renormalization of twist-2 operators and the perturbative calculation of their anomalous dimensions. The main approach implemented in this thesis is to consider the theory at its critical point, where the Poincaré symmetry is enhanced to the full conformal group, and subsequently relate the results to the physical theory. We exploit this approach in two ways. First, we argue that the structure of the analytic continuation of the CFT spectrum in spin constrains the analytic structure of anomalous dimensions. These constraints in turn allow us to predict the singular behavior and perform an all-order resummation of certain singular contributions. We verify this framework in a variety of theories, including six-dimensional φ3 -type models, the O(N )-symmetric φ4 model, and the Gross–Neveu–Yukawa model. The second application concerns the collinear conformal symmetry, which is exact at the critical point, and constrains the evolution of exclusive QCD processes. These constraints, together with the use of conformal Ward identities, allow us to calculate the evolution kernel of the transversity quark operator at three-loop order.