The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Spectrum of the QCD Dirac operator and chiral random matrix theory
Open accessAbstract
We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of the classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble, the chiral unitary ensemble, and the chiral symplectic ensemble. They correspond to gauge groups SU(2) in the fundamental representation, SU(${\mathit{N}}_{\mathit{c}}$), ${\mathit{N}}_{\mathit{c}}$\ensuremath{\ge}3 in the fundamental representation, and non-Abelian gauge groups SU(${\mathit{N}}_{\mathit{c}}$) for all ${\mathit{N}}_{\mathit{c}}$ with fermions in the adjoint representation, respectively. The joint probability density reproduces Leutwyler-Smilga sum rules.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
Bohigas, O., Giannoni, M. J., & Schmit, C. (1984) · Physical Review Letters · doi:10.1103/physrevlett.52.1 · Cited by 2,750
Statistical Theory of the Energy Levels of Complex Systems. I
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703773 · Cited by 2,266
Chiral symmetry breaking in confining theories
Banks, T., & Casher, A. (1980) · Nuclear Physics B · doi:10.1016/0550-3213(80)90255-2 · Cited by 884
Spectrum of Dirac operator and role of winding number in QCD
Leutwyler, H., & Smilga, A. (1992) · Physical Review D · doi:10.1103/physrevd.46.5607 · Cited by 696
The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703863 · Cited by 664
Random matrix theory and spectral sum rules for the Dirac operator in QCD
Shuryak, E. V., & Verbaarschot, J. J. M. (1993) · Nuclear Physics A · doi:10.1016/0375-9474(93)90098-i · Cited by 512
Self-citationThe alignment of the vacuum in theories of technicolor
Peskin, M. E. (1980) · Nuclear Physics B · doi:10.1016/0550-3213(80)90051-6 · Cited by 407
Spectral density of the QCD Dirac operator near zero virtuality
Verbaarschot, J. J. M., & Zahed, I. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.3852 · Cited by 388
Self-citationRandom matrices and information theory
Balian, R. (1968) · Il Nuovo Cimento B · doi:10.1007/bf02710326 · Cited by 160
Cited by
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
Altland, A., & Zirnbauer, M. R. (1997) · Physical Review B · doi:10.1103/physrevb.55.1142 · Cited by 2,402
JT gravity and the ensembles of random matrix theory
Stanford, D., & Witten, E. (2020) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2020.v24.n6.a4 · Cited by 303
Metadata
- Authors
- Verbaarschot, J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1994-04-18
- Volume
- 72
- Issue
- 16
- Pages
- 2531-2533
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2601300439
- Cited by
- 459
- References
- 9
- FWCI
- 9.64
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Spectrum of the QCD Dirac operator and chiral random matrix theory. https://app.cochat.ai/papers/10.1103/physrevlett.72.2531
- The paper
- Verbaarschot, J. (1994). Spectrum of the QCD Dirac operator and chiral random matrix theory. Physical Review Letters. https://doi.org/10.1103/physrevlett.72.2531
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
