期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 47, 期 29, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/47/29/295201
关键词
random matrix theory; supersymmetry; multivariate statistics; correlated Wishart matrices; universality; chiral Lagrangian; multicritical ensembles
资金
- Deutsche Forschungsgemeinschaft 'Symmetries and Universality in Mesoscopic Systems' [Sonderforschungsbereich Transregio 12]
- Alexander von Humboldt foundation
In the past few years, the supersymmetry method has been generalized to real symmetric, Hermitian, and Hermitian self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic groups, respectively. We extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way. Thereby we generalize a projection formula providing a direct link and, hence, a 'short cut' between the probability density in ordinary space and that in superspace. We emphasize that this point was one of the main problems and shortcomings of the supersymmetry method, since only implicit dualities between ordinary space and superspace were known before. To provide examples, we apply this approach to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy) ensemble and an ensemble with a quartic potential. Moreover, we consider the partially quenched partition function of the three chiral Gaussian ensembles corresponding to four-dimensional continuum quantum chromodynamics. We identify a natural splitting of the chiral Lagrangian in its lowest order into a part for the physical mesons and a part associated with source terms generating the observables, e.g. the level density of the Dirac operator.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据