Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD

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Among the non-perturbative properties of quarks, those associated with the topology of the gauge fields occupy a special place. This follows from the Atiyah-Singer index theorem which guarantees the existence of fermionic zero modes on configurations with non-trivial topology. As a result, non-perturbative issues related to the axial anomaly can generally be studied with enhanced control. In the context of finite temperature QCD, one such issue relates to the realization of the anomalous U(1) axial symmetry. If this symmetry were to be effectively restored at the critical temperature, the increased number of soft degrees of freedom would modify the nature ... continued below

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5 p.

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Kogut, J.B.; Lagaee, J.F. & Sinclair, D.K. October 1, 1997.

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Among the non-perturbative properties of quarks, those associated with the topology of the gauge fields occupy a special place. This follows from the Atiyah-Singer index theorem which guarantees the existence of fermionic zero modes on configurations with non-trivial topology. As a result, non-perturbative issues related to the axial anomaly can generally be studied with enhanced control. In the context of finite temperature QCD, one such issue relates to the realization of the anomalous U(1) axial symmetry. If this symmetry were to be effectively restored at the critical temperature, the increased number of soft degrees of freedom would modify the nature of the phase transition. Needless to say, only the lattice can really hope to tackle this question, at this time. Unfortunately, the lattice formulation also introduces artifacts and there is for example no exact index theorem in this context. Instead, what is observed with the actions currently used is the zero mode shift phenomenon (i.e. modes with small but non-zero eigenvalue and which are not exactly chiral). What the authors would like to show here is that even in this case, enough is recognizable of the continuum behavior that meaningful conclusions can be drawn. They find that the U{sub A}(1) symmetry is not restored at the phase transition but only at somewhat higher temperatures. At the same time, it is clear that detailed quantitative questions could only be answered with the use of an improved action.

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5 p.

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INIS; OSTI as DE98050376

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  • 15. international symposium on lattice field theory (Lattice-15), Edinburgh (United Kingdom), 22-26 Jul 1997

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  • Other: DE98050376
  • Report No.: ANL-HEP-CP--97-74
  • Report No.: CONF-970709--
  • Grant Number: W-31109-ENG-38
  • Office of Scientific & Technical Information Report Number: 658331
  • Archival Resource Key: ark:/67531/metadc708484

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  • October 1, 1997

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • Aug. 23, 2016, 3:48 p.m.

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Kogut, J.B.; Lagaee, J.F. & Sinclair, D.K. Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD, article, October 1, 1997; United States. (digital.library.unt.edu/ark:/67531/metadc708484/: accessed May 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.