theta dependence of SU(N) gauge theories in the presence of a topological term

We investigate a new numerical procedure to compute fermionic correlation functions at very small quark masses. Large statistical fluctuations, due to the presence of local ``bumps'' in the wave functions associated with the low-lying eigenmodes of the Dirac operator, are reduced by an exact low-mode averaging. To demonstrate the feasibility of the technique, we compute the two-point correlator of the left-handed vector current with Neuberger fermions in the quenched approximation, for lattices with a linear extent of L ≈ 1.5 fm, a lattice spacing a ≈ 0.09 fm, and quark masses down to the -regime. By matching the results with the corresponding (quenched) chiral perturbation theory expressions, an estimate of (quenched) low-energy constants can be obtained. We find agreement between the quenched values of F extrapolated from the p-regime and extracted in the -regime.

Low-energy couplings of QCD from current correlators near the chiral limit

We review results concerning the theta dependence of 4D SU(N) gauge theories and QCD, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss theta dependence in the large-N limit. 
Most results have been obtained within the lattice formulation of the theory via numerical simulations, which allow to investigate the theta dependence of the ground-state energy and the spectrum around theta=0 by determining the moments of the topological charge distribution, and their correlations with other observables. We discuss the various methods which have been employed to determine the topological susceptibility, and higher-order terms of the theta expansion. We review results at zero and finite temperature. We show that the results support the scenario obtained by general large-N scaling arguments, and in particular the Witten-Veneziano mechanism to explain the U(1)_A problem. We also compare with results obtained by other approaches, especially in the large-N limit, where the issue has been also addressed using, for example, the AdS/CFT correspondence. 
We discuss issues related to theta dependence in full QCD: the neutron electric dipole moment, the dependence of the topological susceptibility on the quark masses, the U(1)_A symmetry breaking at finite temperature. 
We also consider the 2D CP(N) model, which is an interesting theoretical laboratory to study issues related to topology. We review analytical results in the large-N limit, and numerical results within its lattice formulation. 
Finally, we discuss the main features of the two-point correlation function of the topological charge density.

Theta dependence of SU(N) gauge theories in the presence of a topological term

A first study of numerical Monte Carlo simulations with two quark doublets, a mass-degenerate one and a mass-split one, interpreted as u, d, s and c quarks, is carried out in the framework of the twisted mass Wilson lattice formulation. Tuning the bare parameters of this theory is explored on 123·24 and 163·32 lattices at lattice spacings a≃0.20 fm and a≃0.15 fm, respectively.

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Numerical simulation of QCD with u, d, s and c quarks in the twisted-mass Wilson formulation

A first study of numerical Monte Carlo simulations with two quark doublets, a mass-degenerate one and a mass-split one, interpreted as u, d, s and c quarks, is carried out in the framework of the twisted mass Wilson lattice formulation. Tuning the bare parameters of this theory is explored on 12^3x24 and 16^3x32 lattices at lattice spacings a=0.20fm and a=0.15fm, respectively.

/pdf/numerical-simulation-of-qcd-with-u-d-s-and-c-quarks-in-the-4a5bta3gvf.pdf

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the \epsilon-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.

Spectral Properties of the Overlap Dirac Operator in QCD

We present simulation results employing overlap fermions for the axial correlation functions in the epsilon-regime of chiral perturbation theory. In this regime, finite size effects and topology play a dominant role. Their description by quenched chiral perturbation theory is compared to our numerical results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm are necessary to interpret the numerical data obtained in distinct topological sectors in terms of the epsilon-expansion. Such lattices are, however, still substantially smaller than the ones needed in standard chiral perturbation theory. However, we also observe severe difficulties at very low values of the quark mass, in particular in the topologically trivial sector.

Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions

We compare the behavior of overlap fermions, which are chirally invariant, and of Wilson twisted mass fermions at full twist in the approach to the chiral limit. Our quenched simulations reveal that with both formulations of lattice fermions pion masses of O(250 MeV) can be reached in practical applications. Our comparison is done at a fixed value of the lattice spacing a=0.123 fm. A number of quantities are measured such as hadron masses, pseudoscalar decay constants and quark masses obtained from Ward identities. We also determine the axial vector renormalization constants in the case of overlap fermions.

Going chiral: overlap versus twisted mass fermions

We study lattice QCD with a gauge action, which suppresses small plaquette values. Thus the MC history is confined to a single topological sector over a significant time, while other observables are decorrelated. This enables the cumulation of statistics with a specific topological charge, which is needed for simulations of QCD in the $\epsilon$-regime. The same action may also be useful for simulations with dynamical quarks. The update is performed with a local HMC algorithm.

Testing a Topology Conserving Gauge Action in QCD

We test a set of lattice gauge actions for QCD that suppress small plaquette values and in this way also suppress transitions between topological sectors. This is well suited for simulations in the e‐regime and it is expected to help in numerical simulations with dynamical quarks.

Lattice Gauge Actions for Fixed Topology

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