Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates

Abstract

Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By introducing $N_v$ fermion species of equal masses, we next use the Virasoro constraints to compute two (low-mass and large-mass) expansions of the partially quenched chiral condensate through the replica method of letting $N_v\to 0$. The low-mass expansion can only be pushed to a certain finite order due to de Wit-'t Hooft poles, but the large-mass expansion can be carried through to arbitrarily high order. Results agree exactly with earlier results obtained through both Random Matrix Theory and the supersymmetric method.

arXiv commentLaTeX, 19 pages, misprints corrected

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Cited by in corpus (28)

• Random Matrix Theory and Chiral Symmetry in QCD
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Replica Limit of the Toda Lattice Equation
• Finite-size Scaling of Meson Propagators
• Finite-Size Scaling of Vector and Axial Current Correlators
• The Chiral Condensate in a Finite Volume
• Quenched Finite Volume Logarithms
• Eigenvalue Distributions of the QCD Dirac Operator
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• QCD3 and the Replica Method
• The Replica Limit of Unitary Matrix Integrals
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Supersymmetric Quenching of the Toda Lattice Equation
• Rate of convergence of linear functions on the unitary group
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Character Expansions for the Orthogonal and Symplectic Groups
• Mesoscopic QCD and the Theta Vacua
• Partially quenched chiral perturbation theory in the epsilon-regime
• Banks-Casher-type relation for the BCS gap at high density
• Interpolation between the epsilon and p regimes
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• The Replica Method and Toda Lattice Equations for QCD_3
• The zeros of the QCD partition function
• Finite Volume Chiral Partition Functions and the Replica Method
• Finite-volume meson propagators in quenched chiral perturbation theory