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.

arXiv comment4+21 pages; v2: details on the ADHM construction added

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• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
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• Anomalous $U(1{)}_A$ couplings and the Columbia plot
• Analysis on nonperturbative flavor violation at chiral crossover criticality in QCD
• Anomalous interactions between mesons with nonzero spin and glueballs
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid
• Nonperturbative Flavor Breaking in Topological Susceptibility at Chiral Crossover
• QCD topology and axion properties in an isotropic hot and dense medium
• Thermal behavior of effective U_A(1) anomaly couplings in reflection of higher topological sectors
• Higher topological charge in the QCD vacuum and axion cosmology
• Detecting scale anomaly in chiral phase transition of QCD: new critical endpoint pinned down
• Electroweak ${\eta }_{\mathrm{w}}$ meson
• ${\eta }_{\mathrm{w}}$-meson from topological properties of the electroweak vacuum
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature