Mesoscopic QCD and the Theta Vacua

Abstract

The partition function of QCD is analyzed for an arbitrary number of flavors, N_f, and arbitrary quark masses including the contributions from all topological sectors in the Leutwyler--Smilga regime. For given N_f and arbitrary vacuum angle, θ, the partition function can be reduced to N_f-2 angular integrations of single Bessel functions. For two and three flavors, the θdependence of the QCD vacuum is studied in detail. For N_f= 2 and 3, the chiral condensate decreases monotonically as θincreases from zero to πand the chiral condensate develops a cusp at θ=πfor degenerate quark masses in the macroscopic limit. We find a discontinuity at θ=πin the first derivative of the energy density with respect to θfor degenerate quark masses. This corresponds to the first--order phase transition in which CP is spontaneously broken, known as Dashen's phenomena.

31 pages, revtex, 10 figures, final version to appear in Nucl. Phys. B

References in corpus (7)

• Solution of the Complex Action Problem in the Potts Model for Dense QCD
• Topological Susceptibility of Yang-Mills Center Projection Vortices
• Quark mass effects on the topological susceptibility in QCD
• Topological Susceptibility in Lattice QCD with Two Flavors of Dynamical Quarks
• Topological susceptibility in full QCD: lattice results versus the prediction from the QCD partition function with granularity
• CP(N-1) Models with Theta Term and Fixed Point Action
• Topological Susceptibility on Dynamical Staggered Fermion Configurations

Cited by in corpus (15)

• SU(N) gauge theories at large N
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
• Singular values of the Dirac operator in dense QCD-like theories
• Deconfinement in Matrix Models about the Gross--Witten Point
• The Chiral Condensate in a Finite Volume
• Cumulants of the QCD topological charge distribution
• Chiral perturbation theory in a theta vacuum
• Dashen's Phenomenon in Gauge Theories with Spontaneously Broken Chiral Symmetries
• The Heisenberg XX spin chain and low-energy QCD
• Chiral symmetry breaking with no bilinear condensate revisited
• Interpolation between the epsilon and p regimes
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• Chiral condensate and Dirac spectrum of one- and two-flavor QCD at nonzero $\theta$-angle
• Phase structure with nonzero ${\Theta }_{\mathrm{QCD}}$ and twisted mass fermions