We compute the condensate in QCD with two flavors of dynamical fermions using numerical simulation. The simulations use overlap fermions, and the condensate is extracted by fitting the distribution of low lying eigenvalues of the Dirac operator in sectors of fixed topological charge to the predictions of Random Matrix Theory.

In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two cells of the pair. Assuming this form for the pair correlations, we make explicit the conditions of statistical independence at large distance. When, on averag...

Topological charge distributions in 2 dimensional CP 2 model with θ-term is calculated. In strong coupling regions, topological charge distribution is approximately given by Gaussian form as a function of topological charge and this behavior leads to the first order phase transition at θ = π. In weak coupling regions it shows non-Gaussian distribution and the first order phase transition disapp...

We analyze the interplay of topological objects in four-dimensional QCD on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This feature is independent of the topological charge definition used. For...

We study the renormalization group evolution up to the xed point of the lattice topological susceptibility in the 2{d O(3) non{linear {model. We start with a discretization of the continuum topological charge by a local charge density, polynomial in the lattice elds. Among the diierent choices we propose also a Symanzik{improved lattice topological charge. We check step by step in the renormali...

We study the spatial correlator of the topological charge density operator in pure SU(3) gauge theory and in two flavor QCD. We show that the data for distances up to about 1 fm is consistent with a vacuum consisting of individual instantons and closely bound pairs. The percentage of paired objects is twice as large on the dynamical configurations than on the pure gauge ones, implying increased...

The square root of the positive definite hermitian operator D† wDw in Neuberger’s proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1 = 1 2 (Yk +D † wDwY −1 k ) with Y0 = 1I, where Y 2 k converges to D † wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investig...

We show that the Skyrme theory possesses a submodel with an infinite number of local conserved currents. The Skyrmions of unit topological charge belong to such integrable sector of the theory. The constraints leading to the submodel explore a decomposition of SU (2) with a complex field parametrizing the symmetric space SU (2)/U (1) and a real field in the direction of U (1). The higher charge...

The random vortex world-surface model is an infrared effective model of Yang-Mills dynamics based on center vortex degrees of freedom. These degrees of freedom carry topological charge through writhe and self-intersection of their world-surfaces. A practical implementation of the model realizes the vortex world-surfaces by composing them of elementary squares on a hypercubic lattice. The topolo...

We rederive and discuss the result of the previous paper that in the standard model θ-term related to W-boson field can not be induced by weak instantons. This follows from the existence of the fermion zero mode in the instanton field even when Yukawa couplings are switched on and there are no massless particles. We consider the new index theorem connecting the topological charge of the weak ga...