Related papers: The zeros of the QCD partition function
We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The…
It is shown that in vector-like gauge theories, such as QCD, and in the limit of a large number of colours Nc, the ordering pattern of narrow vector and axial-vector states at low energies is correlated with the size of the possible local…
In this paper, we consider the nontrivial zeros of the Riemann zeta function as the eigenvalues of the Dirac operator on a fractal manifold. From the heat kernel expansion, we figure out that the fractal dimension of the manifold is about…
The chiral phase transition of QCD is analyzed in a model combining random matrix elements of the Dirac operator with specially chosen non-random ones. The special form of the latter is motivated by the assumption that the fermionic…
Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero…
We review important aspects of QCD in the continuum and on the lattice and take a look at the fate of its symmetries with an emphasis on chiral symmetry breaking on the lattice.
We review recent results on the phase structure of QCD and bulk QCD thermodynamics. In particular we discuss how universal critical scaling related to spontaneous breaking of the chiral symmetry manifests itself in recent lattice QCD…
We describe the occurrence and physical role of zero-energy modes in the Dirac equation with a topologically non-trivial background.
We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of…
Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential ($\mu_B$) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature…
I review recent progress achieved on the lattice in the quantitative comprehension of chiral symmetry breaking in QCD. Emphasis is given to the recent precise computations of the spectral density of the Dirac operator in the continuum…
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincar\'e generators), while the vacuum state is a chiral invariant. This property is used to give a…
While it has been well-known that the chirality is an important symmetry for Dirac-fermion systems that gives rise to the zero-mode Landau level in graphene, here we explore whether this notion can be extended to tilted Dirac cones as…
We investigate the contribution that instantons make to the QCD chiral condensate for Nf= 0, 1 and 2 quark flavours. We use a simplified model: the instantons are a (weighted) gas, the fermionic integrations are restricted to the subspace…
We present a generalized circle theorem which includes the Lee-Yang theorem for symmetric transitions as a special case. It is found that zeros of the partition function can be written in terms of discontinuities in the derivatives of the…
We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition…
The formulation of QCD which contains no divergences and no renormalization procedure is presented. It contains both perturbative and non-perturbative phenomena. It is shown that, due to its asymptotically free nature, the theory is not…
Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An…
We propose a new method for the study of the chiral properties of the ground state in QFT's based on the computation of the probability distribution function of the chiral condensate. It can be applied directly in the chiral limit and…
At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is…