The Myriad Uses of Instantons

Abstract

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 $2N_f|Q|$ quarks, which for $Q=1$ make the ${\eta }^{\prime }$ heavy. For two flavors we compute an anomalous quartic meson coupling and discuss its implications for the phenomenology of the chiral phase transition. A dilute instanton gas suggests that for cold, dense quarks, instantons do not evaporate until very high densities, when the baryon chemical potential is $\gtrsim 2$ GeV.

Comments: 4+21 pages; v2: details on the ADHM construction added