Monopole and instanton effects in QCD


Seminar “Theory of Hadronic Matter under Extreme Conditions”

Date and Time: Wednesday, 7 April 2021, at 4:00 PM

Venue: Online conference in Zoom, Bogoliubov Laboratory of Theoretical Physics

Seminar topic: “Monopole and instanton effects in QCD”

Speaker: Masayasu Hasegawa


This research project aims to reveal the effects of magnetic monopoles and instantons in QCD on observables. Monopoles cause quark confinement through condensations in the QCD vacuum, and instantons induce chiral symmetry breaking. The monopoles and instantons closely relate to each other and interact among quarks and gluons in the QCD vacuum. It is not easy to show the relations and interactions among them by phenomenological computations because of the strong interaction in the low-energy of QCD. Therefore, we perform the numerical simulations of lattice gauge theory.

We first add a pair of monopole and anti-monopole, varying the magnetic charges of the monopole and anti-monopole, to the QCD vacua. We then numerically calculate the observables using the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory. The renormalization constants for the chiral condensate, quark masses, and decay constants are considered. We compare the numerical results with the predictions in the random matrix theory, instanton liquid model, instanton vacuum, etc., and evaluate the effects on the observables.

We have found that the additional monopoles and anti-monopoles make instantons and anti-instantons without changing the vacuum structure [1]. We discover the effects of the created instantons and anti-instantons on the observables with increasing the number density of instantons and anti-instantons as follows [2]: the chiral condensate (negative values) decreases, light quark masses become heavy, and decay constants and masses of the light mesons increase. The decay width and lifetime of the charged pion are estimated using these outcomes. The decay width of the charged pion becomes wider than the experiment, and the lifetime of the charged pion becomes shorter than the experiment. Finally, we obtain quantitative relations among these observables and the number density of instantons and anti-instantons.

In this seminar, I will talk about new research results [2].

[1] A. Di Giacomo and M. Hasegawa, Instantons and monopoles, Phys. Rev. D 91, 054512 (2015).
[2] M. Hasegawa, Monopole and instanton effects in QCD, J. High Energ. Phys. 2020, 113 (2020).