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.
Highlights
Matrix integrals appear in diverse fields of mathematics and theoretical physics
In quantum chromodynamics (QCD), due to spontaneous breaking of chiral symmetry, the low-energy physics may be described by a nonlinear sigma model
It is known since olden times that there are three patterns of chiral symmetry breaking in QCD, depending on the representation of quarks [15]
Summary
Matrix integrals appear in diverse fields of mathematics and theoretical physics (see [1,2] for reviews). The list of most well-studied unitary matrix integrals includes, but is not limited to, the Brezin-Gross-Witten integral [6,7] ( known as the Leutwyler-Smilga integral [8]), the Harish-Chandra-Itzykson-Zuber integral [9,10], and the Berezin-Karpelevich integral [11,12,13] They are relevant to quantum gravity, lattice gauge theory, quantum chromodynamics (QCD), quantum chaos, and disordered mesoscopic systems.
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