The Myriad Uses of Instantons

Understand

In quantum chromodynamics (QCD), the role which topologically non-trivial configurations play in splitting the singlet pseudo-Goldstone meson, the $\eta^\prime$, from the octet is familiar.

• In addition, such configurations contribute to other processes which violate the axial $U(1)_A$ symmetry.
• While the nature of topological fluctuations in the confined phase is still unsettled, at temperatures well above that for the chiral phase transition, they can be described by a dilute gas of instantons.
• We show that instantons of arbitrary topological charge $Q$ generate anomalous interactions between $2 N_f |Q|$ quarks, which for $Q = 1$ make the $\eta^\prime$ heavy.