Related papers: Universal Spectral Correlators and Massive Dirac O…
To any differential system $d\Psi=\Phi\Psi$ where $\Psi$ belongs to a Lie group (a fiber of a principal bundle) and $\Phi$ is a Lie algebra $\mathfrak g$ valued 1-form on a Riemann surface $\Sigma$, is associated an infinite sequence of…
We study two $1/N_c$ effects on the meson spectra by using the AdS/CFT correspondence where the $1/N_c$ corrections from the chiral condensate and the quark density are controlled by the gravitational backreaction of the massive scalar…
Macroscopic properties of the strong interaction near its chiral phase transition exhibit scaling behaviors, which are the same as those observed close to the magnetic transition in a 3-dimensional classical spin system with $O(4)$…
The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…
Recently, Kalkreuter obtained the complete Dirac spectrum for an $SU(2)$ lattice gauge theory with dynamical staggered fermions on a $12^4$ lattice for $\beta =1.8$ and $\beta=2.8$. We performed a statistical analysis of his data and found…
We use a chiral random matrix model with 2N_f flavors to mock up the QCD Dirac spectrum at finite chemical potential. We show that the 1/N approximation breaks down in the quenched state with spontaneously broken chiral symmetry. The…
We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the…
We review some recent results concerning the quantitative analysis of the universality classes of two-dimensional statistical models near their critical point. We also discuss the exact calculation of the two--point correlation functions of…
We present a systematic procedure to establish a connection between complex neutrino mass matrix textures and experimental observables, including the Dirac CP phase. In addition, we illustrate how future experimental measurements affect the…
We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from…
We compute the spectrum of SU(2) gauge theory with two, four or six Dirac fermions in the fundamental representation of the gauge group. We investigate the scaling of the meson masses as a function of the quark mass when approaching the…
We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws…
We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…
We discuss models of neutrino masses that lead to a large mixing angle for atmospheric neutrino oscillations. In particular we study a mechanism where a simple texture for the Dirac matrix leads to the observed pattern of mixings for a…
We demonstrate the level statistics in the vicinity of the Anderson transition in $d>2$ dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of…
Properties of universality have essential relevance for the theory of random matrices usually called the Wigner ensemble. The issue was analysed up to recent years with detailed and relevant results. We present a slightly different view and…
We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the…
We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following…
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…
We present results on hadron masses and quark condensate from Neuberger's overlap fermion. The scaling and chiral properties and finite volume effects from this new Dirac operator are studied. We find that the generalized…