Comment on Dirac spectral sum rules for QCD_3

TL;DR

This paper critiques recent claims about Dirac spectral sum rules in 3D gauge theories, demonstrating their inaccuracies and contradictions with established results from random matrix theory.

Contribution

It provides a critical analysis showing the previous computations are incorrect and conflicts with known exact spectral density results.

Findings

Previous sum rule computations are incorrect.

Contradictions with exact spectral density results.

Supports validity of random matrix theory in this context.

Abstract

Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000); Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point out that these computations are incorrect, and that they contradict with the exact results for the spectral densities unambiguously derived from random matrix theory by Nagao and myself.