Low-Lying Dirac Eigenmodes, Topological Charge Fluctuations and the Instanton Liquid Model.pdf

a r X i v : h e p - l a t / 0 2 0 5 0 1 2 v 1 7 M a y 2 0 0 2 LOW-LYING DIRAC EIGENMODES, TOPOLOGICAL CHARGE FLUCTUATIONS AND THE INSTANTON LIQUID MODEL I. HORVA?TH, S.J. DONG, T. DRAPER Department of Physics Astronomy University of Kentucky, Lexington, KY 40503, USA F.X. LEE Center for Nuclear Studies and Department of Physics George Washington University Washington, DC 20052, USA, and Jefferson Laboratory, Newport News, VA 23606, USA H.B. THACKER Department of Physics University of Virginia, Charlottesville, VA 22901, USA AND J.B. ZHANG CSSM and Department of Physics and Mathematical Physics University of Adelaide, Adelaide, SA 5005, Australia Abstract. The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of ’t Hooft “would-be” zeromodes associated with in- stanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry break- ing in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological “would-be” zero- modes could be associated. Presented by I. Horva?th at the NATO Advanced Research Workshop “Confinement, Topology, and other Non-Perturbative Aspects of QCD”, January 21-27, 2002, Stara? Lesna? (Slovakia). 21. Introduction The idea of the instanton-dominated QCD vacuum appeared shortly af- ter the discovery of the instanton [1]. In particular, the instanton gas pic- ture [2] populates the vacuum with well-separated instantons which, using semiclassical methods, leads to the possible qualitative resolution of the U(1) problem [3], as well as to the conclusion that QCD physics depends on the θ-parameter [4]. However, it became clear very soon that QCD is not semiclassical in this sense because the instanton gas picture does not lead to confin