Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology

Abstract

We investigate the topological properties of unquenched $QCD$ on the basis of numerical results of simulations at fixed topological charge, recently reported by Borsanyi et al.. We demonstrate that their results for the mean value of the chiral condensate at fixed topological charge are inconsistent with the analytical prediction of the large volume expansion around the saddle point, and argue that the most plausible explanation for the failure of the saddle point expansion is a vacuum energy density $\theta$-independent at high temperatures, but surprisingly not too high $(T\sim 2T_c)$, a result which would imply a vanishing topological susceptibility, and the absence of all physical effects of the $U(1)$ axial anomaly at these temperatures. We also show that under a general assumption concerning the high temperature phase of $QCD$, where the $SU(N_f{)}_A$ symmetry is restored, the analytical prediction for the chiral condensate at fixed topological charge is in very good agreement with the numerical results of Borsanyi et al., all effects of the axial anomaly should disappear, the topological susceptibility and all the $\theta$-derivatives of the vacuum energy density vanish and the theory becomes $\theta$-independent at any $T>T_c$ in the infinite volume limit.

arXiv comment18 pages, no figures, typos added in section 4, small changes in the text and some references added

References in corpus (25)

• Exactly massless quarks on the lattice
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• More about exactly massless quarks on the lattice
• The index theorem in QCD with a finite cut-off
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• The topological susceptibility in finite temperature QCD and axion cosmology
• Axion phenomenology and $\theta$-dependence from $N_f=2+1$ lattice QCD
• Finite volume QCD at fixed topological charge
• Lattice QCD input for axion cosmology
• The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
• Axion cosmology, lattice QCD and the dilute instanton gas
• Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature
• Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation
• QCD at Fixed Topology
• The High Temperature Phase of QCD and {\boldmath $U(1{)}_A$} Symmetry
• Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
• Which Chiral Symmetry is Restored in High Temperature QCD?
• Topological susceptibility at high temperature on the lattice
• Theta dependence of the deconfinement temperature in Yang-Mills theories
• $\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation
• Phase diagram of Yang-Mills theories in the presence of a theta term
• The 4D SU(3) gauge theory with an imaginary theta term
• Anomalous Chiral Symmetry Breaking above the QCD Phase Transition
• Why PQ?
• Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions

Cited by in corpus (12)

• Evidence of effective axial U(1) symmetry restoration at high temperature QCD
• Axions, Instantons, and the Lattice
• Chiral and $U(1{)}_A$ restoration for the scalar/pseudoscalar meson nonets
• Patterns and partners for chiral symmetry restoration
• Massive Schwinger model at finite $\theta$
• Topology in the SU(N_f) chiral symmetry restored phase of unquenched QCD and axion cosmology II
• Axial U(1) symmetry, topology, and Dirac spectra at high temperature in $N_f=2$ lattice QCD
• Light quarks at finite temperature: chiral restoration and the fate of the $U(1{)}_A$ symmetry
• Interplay between $SU(N_f)$ chiral symmetry, $U(1{)}_A$ axial anomaly and massless bosons
• Spectral density of the Dirac-Ginsparg-Wilson operator, chiral $U(1{)}_A$ anomaly, and analyticity in the high temperature phase of $QCD$
• The role of strangeness in chiral and $U(1{)}_A$ restoration
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature