Chiral symmetry, the topological charge and the Yang-Mills gradient flow

Dr. Martin L├╝scher (CERN)

Date(s) - 20/01/2023
14:00 - 15:00

video conference (zoom)

This talk is about an old issue that arose after the instantons were discovered and numerical lattice gauge theory became a popular subject. The question is whether the division of the field space in topological sectors is a property of QCD at the fully non-perturbative level or merely an emergent asymptotic feature of the theory in the semi-classical limit. Exactly how the topological susceptibility and the higher moments of the topological charge distribution are defined beyond the semi-classical level is in fact not obvious, since the formal expressions for the moments are manifestly ultraviolet-divergent. Important conceptual developments in lattice QCD (formulations preserving chiral symmetry and the proof of the finiteness of the Yang-Mills gradient flow) eventually permitted the question to be answered and moreover led to expressions for the moments, which are finite, regularization-independent and consistent with the chiral Ward identities.