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Local Topological and Chiral Properties of Qcd
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pérez, Margarita García Hetrick, James E. Laermann, E. Lagae, Jacques Stamatescu, Ion O. |
| Copyright Year | 1998 |
| Abstract | To elucidate the role played by instantons in chiral symmetry breaking, we explore their properties, in full QCD, around the critical temperature. We study in particular spatial correlations between low-lying Dirac eigenmodes and instantons. Our measurements are compared with the predictions of instanton-based models. We have examined the local topological structure of full QCD and its impact on the physics of chiral symmetry breaking and restoration, by comparing the local topological structure obtained by improved cooling[1], with the lowest eigenmodes of the Dirac operator on the same (uncooled) lattices. We use a set of dynamical finite temperature N t = 12 (MILC[2]) lattices spanning the chiral phase transition, and have extracted the lowest 8 eigenmodes and eigenvalues of the staggered Dirac operator. To summarize our findings, we see: • agreement with the Banks-Casher relationship using the density of eigenvalues near zero (not discussed in this writeup). • good correlation (∼ 70% level) between the spatial structure of zero modes and instantons. • some space-time asymmetry in the local topo-logical susceptibility above T c (and not below), the underlying mechanism of which is under further investigation. To illustrate the relationship between instan-tons and the zero modes of the Dirac operator we show in Figures 2 and 3, the topological charge density F ˜ F (x), on a configuration obtained after 150 sweeps of improved cooling. The timeslice shown happens to contain part of an instanton and anti-instanton, and we plot isosurfaces of positive and negative values of F ˜ F (x). On this cooled configuration, we identify the lowest eigenmode of the Dirac operator; an isosur-face of the magnitude of the eigenvector is plotted along with F ˜ F (x), and is shown in Figure 2. We see that on this smooth configuration in which the UV fluctuations have been removed, | ¯ ψψ(x)| follows F ˜ F (x) exactly, showing that on continuum like configurations, the zero mode " tracks " the topology, as expected from continuum arguments. Next, Figure 3b compares the uncooled zero mode to the cooled topological charge; we see surprisingly good correlation, even after many (150) cooling sweeps. Cooling identifies the dominant instanton—anti-instanton (I-A) pairs and the ensemble correlation between the uncooled Dirac mode and cooled topological charge density is about 70%, after 150 sweeps of improved cooling , on configurations containing one or more I-A pairs. This validates a posteriori the improved cooling process; the … |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-lat/9810033v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Anatomy, Regional Arabic numeral 0 Circuit restoration Computer cooling Cool - action Dirac delta function Dirac operator Dynamical system Emoticon Extraction File spanning Hypertrophy/chronic infection tonsils and adenoid Normal mode Pin grid array Symmetry breaking Telling untruths Topography Topological quantum number Track (course) Triune continuum paradigm UV mapping metric ton |
| Content Type | Text |
| Resource Type | Article |
