A comment on instantons and their fermion zero modes in adjoint QCD_2
| Autor: | Andrei V. Smilga |
|---|---|
| Přispěvatelé: | Laboratoire de physique subatomique et des technologies associées (SUBATECH), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Instanton Zero mode QC1-999 High Energy Physics::Lattice fermion: zero mode FOS: Physical sciences General Physics and Astronomy 01 natural sciences topological Gauge group 0103 physical sciences quantum chromodynamics Gauge theory Invariant (mathematics) 010306 general physics Mathematical physics Physics 010308 nuclear & particles physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] High Energy Physics::Phenomenology Zero (complex analysis) deformation Fermion Gauge (firearms) SU(N)/Z(N) High Energy Physics - Theory (hep-th) confinement flux: magnetic instanton transformation: gauge |
| Zdroj: | SciPost Physics SciPost Physics, SciPost Foundation, 2021, 10 (6), pp.152. ⟨10.21468/SciPostPhys.10.6.152⟩ SciPost Physics, Vol 10, Iss 6, p 152 (2021) |
| ISSN: | 2542-4653 |
| DOI: | 10.21468/SciPostPhys.10.6.152⟩ |
| Popis: | The adjoint 2-dimensional $QCD$ with the gauge group $SU(N)/Z_N$ admits topologically nontrivial gauge field configurations associated with nontrivial $\pi_1[SU(N)/Z_N] = Z_N$. The topological sectors are labelled by an integer $k=0,\ldots, N-1$. However, in contrast to $QED_2$ and $QCD_4$, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of $k(N-k)$ zero mode doublets in the topological sector $k$. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the mod. 2 conjecture. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed. Comment: minor changes, a reference added. 28 pages, 3 figures |
| Databáze: | OpenAIRE |
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