Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover
High Energy Physics - Theory
2021-06-08 v3 Mathematical Physics
math.MP
Abstract
A unitary matrix integral that appears in the low-energy limit of QCD-like theories with quarks in real representations of the gauge group at finite chemical potential is analytically evaluated and expressed as a pfaffian. Its application to the GOE-GUE crossover in random matrix theory is discussed. An analogous unitary integral for QCD-like theories with quarks in pseudoreal representations of the gauge group is also evaluated.
Keywords
Cite
@article{arxiv.2006.10242,
title = {Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover},
author = {Takuya Kanazawa},
journal= {arXiv preprint arXiv:2006.10242},
year = {2021}
}
Comments
6 pages. v2: section 5 added. The proof of eq.(49) has been published in Phys.Lett.B 819 (2021) 136416 at https://doi.org/10.1016/j.physletb.2021.136416