Abstract
Abstract
We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference92 articles.
1. G. Akemann, J. Baik, and P. Di Francesco eds., The Oxford Handbook of Random Matrix Theory, Oxford University Press, Oxford U.K. (2011).
2. E.V. Shuryak and J.J.M. Verbaarschot, Random matrix theory and spectral sum rules for the Dirac operator in QCD, Nucl. Phys.
A 560 (1993) 306 [hep-th/9212088] [INSPIRE].
3. J.J.M. Verbaarschot and I. Zahed, Spectral density of the QCD Dirac operator near zero virtuality, Phys. Rev. Lett.
70 (1993) 3852 [hep-th/9303012] [INSPIRE].
4. J.J.M. Verbaarschot and I. Zahed, Random matrix theory and QCD in three-dimensions, Phys. Rev. Lett.
73 (1994) 2288 [hep-th/9405005] [INSPIRE].
5. J. Gasser and H. Leutwyler, Thermodynamics of Chiral Symmetry, Phys. Lett.
B 188 (1987) 477 [INSPIRE].
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献