The Replica Method and Toda Lattice Equations for QCD_3

Abstract

We consider the epsilon-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these Toda equations allows us to derive the microscopic spectral correlation functions for the QCD Dirac operator in 3 dimensions. For an even number of flavors we reproduce known results derived using other techniques. In the case of an odd number of flavors the theory has a severe sign problem, and we obtain previously unknown microscopic spectral correlation functions.

18 pages, 2 figures

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Cited by in corpus (6)

• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• QCD in One Dimension at Nonzero Chemical Potential
• The Realization of the Sharpe-Singleton Scenario
• The Microscopic Twisted Mass Dirac Spectrum
• Handbook Article on Applications of Random Matrix Theory to QCD
• Finite Volume Gauge Theory Partition Functions in Three Dimensions