The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights

Kaymak V, Kieburg M, Guhr T (2014)
Journal of Physics A Mathematical and Theoretical 47(29).

Journal Article | Published | English

No fulltext has been uploaded

Author
; ;
Abstract
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.
Publishing Year
ISSN
eISSN
PUB-ID

Cite this

Kaymak V, Kieburg M, Guhr T. The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights. Journal of Physics A Mathematical and Theoretical. 2014;47(29).
Kaymak, V., Kieburg, M., & Guhr, T. (2014). The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights. Journal of Physics A Mathematical and Theoretical, 47(29).
Kaymak, V., Kieburg, M., and Guhr, T. (2014). The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights. Journal of Physics A Mathematical and Theoretical 47.
Kaymak, V., Kieburg, M., & Guhr, T., 2014. The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights. Journal of Physics A Mathematical and Theoretical, 47(29).
V. Kaymak, M. Kieburg, and T. Guhr, “The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights”, Journal of Physics A Mathematical and Theoretical, vol. 47, 2014.
Kaymak, V., Kieburg, M., Guhr, T.: The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights. Journal of Physics A Mathematical and Theoretical. 47, (2014).
Kaymak, Vural, Kieburg, Mario, and Guhr, Thomas. “The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights”. Journal of Physics A Mathematical and Theoretical 47.29 (2014).
This data publication is cited in the following publications:
This publication cites the following data publications:

Export

0 Marked Publications

Open Data PUB

Web of Science

View record in Web of Science®

Sources

Inspire 1281732

Search this title in

Google Scholar