Related papers: Dirac operator spectral density and low energy sum…
When chiral symmetry is spontaneously broken, the low-energy part of the Dirac operator spectrum can be computed analytically in the chiral limit. The tool is effective field theory or, equivalently in this case, Random Matrix Theory.
This paper summarizes the recent calculations of the masses and decay constants of the pseudoscalar mesons at the two-loop level, or NNLO, in Partially Quenched Chiral Perturbation Theory (PQxPT). Possible applications include chiral…
The Banks--Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in…
Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative,…
We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of classical random matrix ensembles of Dyson we have three distinct classes: the chiral orthogonal ensemble…
We apply a complex chiral random matrix model as an effective model to QCD with a small chemical potential at zero temperature. In our model the correlation functions of complex eigenvalues can be determined analytically in two different…
A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global…
The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the…
We present our preliminary results for three-point correlation functions involving the operators entering the $\Delta{S}=1$ effective Hamiltonian with an active charm quark, obtained using overlap fermions in the quenched approximation.…
We study physics at temperatures just above the QCD phase transition (Tc) using chiral (overlap) Fermions in the quenched approximation of lattice QCD. Exact zero modes of the overlap Dirac operator are localized and their frequency of…
The relation between the chiral quark condensate in QCD sum rules and chiral perturbation theory is clarified with the help of a low-energy theorem for the scalar and pseudoscalar correlation functions. It is found that the quark condensate…
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue correlations are…
Random Matrix Theory has been a unifying approach in physics and mathematics.In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview…
We investigate and compute spectral sums of the Wilson lattice Dirac operator for quenched SU(3) gauge theory. It is demonstrated that there exist sums which serve as order parameters for the confinement-deconfinement phase transition and…
The low lying spectrum of QCD in the delta-regime is calculated here in chiral perturbation theory up to NNL order. The spectrum has a simple form in terms of the pion decay constant F and a combination of the low energy constants Lambda1…
A recent Monte Carlo study of {\em quenched} QCD showed that the chiral condensate is non-vanishing above $T_c$ in the phase where the average of the Polyakov loop $P$ is complex. We show how this is related to the dependence of the…
The low-energy QCD theorems are generalized in the presence of a constant magnetic field H. Two-loop approximation for the vacuum energy density in the framework of the chiral perturbation theory was obtained and the quark and gluon…
We examine the behavior of the spectral function for the trace of the stress tensor in QCD in the two regimes where it is possible to make analytical progress; weak coupling, and close to a second order QCD phase transition. We determine…
Two different matrix models for QCD with a non-vanishing quark chemical potential are shown to be equivalent by mapping the corresponding partition functions. The equivalence holds in the phase with broken chiral symmetry. It is exact in…
We present the comparison of the analytical microscopic spectral density for lattice QCD with $N_{\rm f}=2$ twisted mass fermions with the one obtained on the lattice utilizing configurations produced by the ETM collaboration. We extract…