RANDOM MATRIX THEORY AND CHIRAL SYMMETRY IN QCD
By J. Verbaarschot, T. Wettig. 2000
296 citations recorded by the source corpus.
▪ Abstract Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of chiral random matrix theory to the QCD partition function. We show that constraints imposed by chiral symmetry and its spontaneous breaking determine the structure of low-energy effective partition functions for the Dirac spectrum. We thus derive exact results for the low-lying eigenvalues of the QCD Dirac operator. We argue that the statistical properties of these eigenvalues are universal and can be described by a random matrix theory with the global symmetries of the QCD partition function. The total number of such eigenvalues increases with the square root of the Euclidean four-volume. The spectral density for larger eigenvalues (but still well below a typical hadronic mass scale) also follows from the same low-energy effective partition function. The valid...
Subfields: Condensed Matter Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b155f8556e19b693521ecb9f5172d408fcc6f734
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In Condensed Matter Physics
In Nuclear and High Energy Physics
Citations in the corpus
- FLAG Review 2019 (2019, methodology): “An alternative strategy is based on the fact that at LO in the ǫ-expansion the partition function in a given topological sector ν is equivalent to the one of a chiral Random Matrix Theory (RMT) [359–362].”