O(N) colour-flavour transformations and characteristic polynomials of real random matrices

TL;DR

This paper derives colour-flavour transformations for the orthogonal group and applies them to compute ensemble averages of characteristic polynomials of real random matrices.

Contribution

It introduces N(O) colour-flavour transformations for the orthogonal group and uses them to analyze characteristic polynomials of real matrices.

Findings

Derived fermionic, bosonic, and supersymmetric colour-flavour transformations for orthogonal group

Calculated ensemble averages of characteristic polynomials of real random matrices

Established a new method for analyzing real random matrix spectra

Abstract

The fermionic, bosonic and supersymmetric variants of the colour-flavour transformation are derived for the orthogonal group. These transformations are then used to calculate the ensemble averages of characteristic polynomials of real random matrices.