Three-dimensional QCD in the adjoint representation and random matrix theory

Details Three-dimensional QCD in the adjoint representation and random matrix theory Three-dimensional QCD in the adjoint representation and random matrix theory

1999-12-21

arxiv.org/abs/hep-th/9912207v3

Phys.Rev. D62 (2000) 016005

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 19 pages. Minor corrections, added comments, to appear on Phys. Rev. D

Scientific paper

10.1103/PhysRevD.62.016005

In this paper we complete the derivations of finite volume partition functions for QCD using random matrix theories by calculating the effective low-energy partition function for three-dimensional QCD in the adjoint representation from a random matrix theory with the same global symmetries. As expected, this case corresponds to Dyson index $\beta =4$, that is, the Dirac operator can be written in terms of real quaternions. After discussing the issue of defining Majorana fermions in Euclidean space, the actual matrix model calculation turns out to be simple. We find that the symmetry breaking pattern is $O(2N_f) \to O(N_f) \times O(N_f)$, as expected from the correspondence between symmetric (super)spaces and random matrix universality classes found by Zirnbauer. We also derive the first Leutwyler--Smilga sum rule.

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