The Chiral Condensate in a Finite Volume

Abstract

Chiral perturbation theory at finite four-volume V (=L^3T) is reconsidered with a view towards finding a computational scheme that can deal with any value of M_πL, where M_πis a generic Nambu-Goldstone mass. The momentum zero modes that cause the usual p-expansion to fail in the chiral limit are treated separately, and partly integrated out to all orders. In this way the theory remains infrared finite in the perturbative expansion, and the chiral limit can be considered at finite volume. We illustrate the technique by computing the quark condensate in a finite volume, smoothly connecting standard results in the p-regime for larger masses with those of the epsilon-regime for smaller masses. From the partially quenched theory we also obtain the spectral density of the Dirac operator, a smooth function from the microscopic region to the bulk region of the p-regime.

33 pages, 10 figures, corrections in (4.7), (6.5), (6.8), additional comment on (3.16)

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Cited by in corpus (33)

• FLAG Review 2019
• Review of lattice results concerning low energy particle physics
• Chiral transition in a finite system and possible use of finite size scaling in relativistic heavy ion collisions
• Prediction for the Mass Spectra of Resonance Mesons in the Soft-Wall AdS/QCD with a Modified 5D Metric
• Determination of the chiral condensate from QCD Dirac spectrum on the lattice
• Determination of the chiral condensate from 2+1-flavor lattice QCD
• Predictive AdS/QCD Model for Mass Spectra of Mesons with Three Flavors
• Volume behaviour of quark condensate, pion mass and decay constant from Dyson-Schwinger equations
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Nambu Jona Lasinio model with proper time regularization in a finite volume
• Infrared-Improved Soft-wall AdS/QCD Model for Mesons
• Probing the chiral regime of Nf=2 QCD with mixed actions
• Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu--Jona-Lasinio model
• Chiral perturbation theory in a theta vacuum
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• Finite Volume at Two-loops in Chiral Perturbation Theory
• Computation of the electromagnetic pion form factor from lattice QCD in the epsilon regime
• Non-perturbative renormalization of bilinear operators with dynamical overlap fermions
• The $\epsilon$-regime of dilaton chiral perturbation theory
• Boundary effects on constituent quark masses and on chiral susceptibility in a four-fermion interaction model
• Interpolation between the epsilon and p regimes
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Nambu-Jona-Lasinio model in a sphere
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Properties of neutral mesons in a hot and magnetized quark matter: size-dependent effects
• Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
• Inverse magnetic catalysis and size-dependent effects on the chiral symmetry restoration
• Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector
• Scalar-glueball-mediated scale-anomaly dominance of the confining pressure of the pion in holographic QCD
• Finite size effect on the thermodynamics of a hot and magnetized hadron resonance gas
• Exploring the Aoki regime
• Finite-size effects and scaling properties of chiral and baryon-number fluctuations
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature