Heriot-Watt Mathematics Report Series
HWM00-22, 28 Sep 2000
Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
R J Szabo
Abstract
The microscopic spectral correlators of the Dirac operator in three-dimensional
Yang-Mills theory coupled to fundamental fermions and with three or more
colours are derived from the supersymmetric formulation of partially quenched
effective Lagrangians. The flavour supersymmetry breaking patterns are
appropriately identified and used to calculate the corresponding finite volume
partition functions from Itzykson-Zuber type integrals over supersymmetric
cosets. New and simple determinant expressions for the spectral correlators in
the mesoscopic scaling region are thereby found. The microscopic spectrum
derived from the effective finite volume partition function of
three-dimensional QCD agrees with earlier results based on the unitary ensemble
of random matrix theory and extends the corresponding calculations for QCD in
four dimensions.
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Publication
R J Szabo
, Microscopic spectrum of the QCD Dirac operator in three dimensions, Nuclear Physics B, 598, 309-347, (2001).
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