QCD3 and the Replica Method

Abstract

Using the replica method, we analyze the mass dependence of the QCD3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fields. Three complementary approaches are considered in this article. First, we derive exact relations between the QCD3 partition function and the QCD4 partition function continued to half-integer topological charge. The replica limit of these formulas results in exact relations between the corresponding microscopic spectral densities of QCD3 and QCD4. Replica calculations, which are exact for QCD4 at half-integer topological charge, thus result in exact expressions for the microscopic spectral density of the QCD3 Dirac operator. Second, we derive Virasoro constraints for the QCD3 partition function. They uniquely determine the small-mass expansion of the partition function and the corresponding sum rules for inverse Dirac eigenvalues. Due to de Wit-'t Hooft poles, the replica limit only reproduces the small mass expansion of the resolvent up to a finite number of terms. Third, the large mass expansion of the resolvent is obtained from the replica limit of a loop expansion of the QCD3 partition function. Because of Duistermaat-Heckman localization exact results are obtained for the microscopic spectral density in this way.

LaTeX, 41 pages. References and some clarifying remarks added

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Cited by in corpus (24)

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• Finite-size Scaling of Meson Propagators
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• Replica treatment of non-Hermitian disordered Hamiltonians
• QCD in One Dimension at Nonzero Chemical Potential
• Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges
• Asymptotics for the partition function in two-cut random matrix models
• Character Expansions for the Orthogonal and Symplectic Groups
• Dirac Spectra of 2-dimensional QCD-like theories
• Random Matrices with Merging Singularities and the Painlevé V Equation
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• New Critical Matrix Models and Generalized Universality
• The Replica Method and Toda Lattice Equations for QCD_3
• Random matrix model for QCD_3 staggered fermions
• Finite Volume Gauge Theory Partition Functions in Three Dimensions
• Toda lattice representation for random matrix model with logarithmic confinement
• Gap Probabilities for Double Intervals in Hermitian Random Matrix Ensembles as $\tau$-Functions -- Spectrum Singularity case
• Random matrix approach to three-dimensional QCD with a Chern-Simons term