Related papers: Universal and non-universal behavior in Dirac spec…
I propose a simple model of the distribution of the small eigenvalues of the QCD Dirac operator well above the finite temperature phase transition where chiral symmetry is restored and the spectral density at zero vanishes. Assuming the…
I derive constraints on the Dirac spectrum in the chirally symmetric phase of a gauge theory with two massless fermion flavors. Using only general properties of correlation functions of scalar and pseudoscalar bilinears, I prove that in the…
In quantum chromodynamics (QCD) at nonzero chemical potential, the eigenvalues of the Dirac operator are scattered in the complex plane. Can the fluctuation properties of the Dirac spectrum be described by universal predictions of…
We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of…
We provide first evidence that Matrix Models describe the low lying complex Dirac eigenvalues in a theory with dynamical fermions at non-zero density. Lattice data for gauge group SU(2) with staggered fermions are compared to detailed…
The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral…
Universality of multicritical unitary matrix models is shown and a new scaling behavior is found in the microscopic region of the spectrum, which may be relevant for the low energy spectrum of the Dirac operator at the chiral phase…
Approximating the sum over all gauge field configurations in the QCD partition function by a liquid of instantons, we calculate the spectrum of the Dirac operator for two and three colors and for 0, 1 and 2 flavors. We find a remarkable…
The distribution of the low-lying QCD Dirac spectrum is analyzed by means of partial quenched chiral perturbation theory. We identify an energy scale below which the valence quark mass dependence of the QCD partition function is given by…
I discuss the consequences of the constraints imposed on the Dirac spectrum by the restoration of chiral symmetry in the chiral limit of gauge theories with two light fermion flavors, with particular attention to the fate of the anomalous…
We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with ${n_\text{D}=4}$…
I study the consequences of chiral symmetry restoration for the Dirac spectrum in finite-temperature gauge theories in the two-flavor chiral limit, using Ginsparg--Wilson fermions on the lattice. I prove that chiral symmetry is restored at…
We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level…
In this talk we review some recent results from random matrix models as applied to some non-perturbative issues in QCD. All of the issues we will discuss touched upon the important phenomenon related to the spontaneous breaking of chiral…
The definition and computation of the topological susceptibility in non-abelian gauge theories is complicated by the presence of non-integrable short-distance singularities. Recently, alternative representations of the susceptibility were…
The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects…
We consider non-Hermitian Dirac operators in QCD-like theories coupled to a chiral U(1) potential or an imaginary chiral chemical potential. We show that in the continuum they fall into the recently discovered universality classes…
We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These…
In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of…
The arbitrary mass scale in the spectral action for the Dirac operator in the spectral action is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms in the spectral action and determine the dilaton couplings.…