Topological Origin of Chiral Symmetry Breaking in QCD and in Gravity

Understand

We show that the assumption of non-zero topological susceptibility of the vacuum in a fermion-free version of a theory, such as gravity or QCD, suffices to conclude the following: Once N massless fermion flavors are added to the theory, they break the chiral flavor symmetry dynamically, down to a subgroup that would be anomaly-free under gauging; In both theories, the pseudo-Goldstone corresponding to axial U(1)-symmetry becomes massive; In QCD as well as in gravity the massless fermions are eliminated from the low energy spectrum of the theory.

• All the above conclusions are reached without making an assumption about confinement.
• Some key methods of our approach are: Reformulation of topological susceptibility in the language of a three-form gauge theory; Utilization of gravity in the role of a spectator interaction for the chiral anomaly-matching in QCD; Gauging chiral symmetries and matching their anomalies using the spectator Green-Schwarz type axions.
• Our observations suggest that breaking of chiral symmetries in QCD and in gravity can be described in unified topological language, and seemingly-disconnected phenomena, such as, the generation of eta'-meson mass in QCD and breaking of global chiral symmetry by gravity may share a secret analogy.