In previous work [1] we showed that the chiral condensate of one flavor QCD shows a Silver Blaze phenomenon when the quark mass crosses $m=0$: The chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator which is dense on the imaginary axis. This behavior is explained in terms of exponentially large cancellations between contributions from the zero mod ... More

The equivalence between the partition function of QCD in the lowest energy limit and the partition function predicted by the Chiral Random Matrix Theory is well established through the use of the Chiral Perturbation Theory. In particular the ChRMT provides a description of the low-lying eigenvalues of the euclidean Dirac operator. In this work we study, on the lattice, the spectrum of the overlap ... More

It is well-known that the continuum Dirac operator and the lattice Dirac operator of staggered fermions do not necessarily share the same global symmetries. For example in three dimensions the continuum Dirac operator satisfies no chiral symmetry while the staggered Dirac operator does. This change of symmetries has a crucial impact on the number and the kind of the lightest pseudo-scalar mesons s ... More

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator ... More

In 2+1 dimensions the global U(2$N$) symmetry associated with massless fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U(2$N$)-invariant limit in interacting fermion models as the domain wall operation is increased. In particular, I will focus on the issue of potential dynamical mass generation in the Thirr ... More

We report last results on anomalous transport in the classical statistical field theory approach. In particular, we studied the chiral plasma instability (CPI) with overlap fermions. From Maxwell and anomalous transport equations, it is expected that those instabilities growth exponentially and only stop when the axial charge decays. Nevertheless, our simulations with Wilson-Dirac and overlap ferm ... More

Using the Sigma model to explore the lowest order pseudoscalar spectrum with SU(3) breaking, I consider an additional exact "taste" symmetry to mimic species doubling. I find that rooting replicas of a valid approach such as Wilson fermions reproduces the desired physical spectrum. In contrast, extra symmetries of the rooted staggered approach leave spurious states and a flavor ... More

It was shown recently that in QCD like theories the chiral transition is accompained by the appearance of localized modes at the low end of the Dirac spectrum. In this talk we show that a crucial ingredient for both phenomena is the ordering of the Polyakov loop which makes the time-slices of the Dirac eigenfunctions correlated. In addition we examine a toy model (R. Frezzotti and G.C. Rossi, P ... More

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coefficient for the CSE in the confining and de-confining phase and investigate possible deviations from t ... More

We compute the topological susceptibility $\chi_t$ of 2+1-flavor lattice QCD employing dynamical Moebius domain-wall fermions, whose residual mass is kept at ∼1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a “slab” sub-volume of the simulated lattice, which was proposed by Bietenholz et al. The quark mass dependence of our results ag ... More

The axion is one of the more interesting candidates to make the dark matter of the universe, and the axion potential plays a fundamental role in the determination of the dynamics of the axion field. Moreover, the way in which the $U(1)_A$ anomaly manifests itself in the chiral symmetry restored phase of $QCD$ at high temperature could be tested when probing the $QCD$ phase transition in relati ... More