I describe a recent calculation (by me, Hoffmann, Liu, and Schaefer) of the chiral condensate in one-flavor QCD using numerical simulations with overlap fermions. The condensate is extracted by fitting the distribution of low lying eigenmodes of the Dirac operator in sectors of fixed topological charge to the predictions of Random Matrix Theory. Our results are in excellent agreement with estim...

The correspondence between topologically stable kinks of scalar $4 theory, vortices of the Abelian Higgs model, monopoles of the 't Hooft-Polyakov model and instantons of SLJ(2) Euclidean gauge theories is exhibited. The use of multi-instanton ansatze for finding multimonopole and multivortex configurations is then investigated. A partial is solution of the N-vortex configurat .ion for the Abel...

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator, or equivalently, as the index of Neuberger’s lattice Dirac operator, is shown to have analogous properties to Lüscher’s geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum lim...

We present preliminary results for a high statistics study of the topological charge distribution in the SU(3) Yang-Mills theory obtained by using the definition of the charge suggested by Neu-berger fermions. We find statistical evidence for deviations from a gaussian distribution. The large statistics required has been obtained by using PCs of the INFN-GRID.

Two-dimensional parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP N−1 sigma model. The Lie-point symmetries of the CP N−1 model are computed for arbitrary N . The Weierstrass formula for immersion is determined and an explicit formula for a moving frame on a surface is constructed. This allows us ...

We analize instanton generated superpotentials for three dimensional N=2 supersymmetric gauge theories obtained by compactifying on S1 N=1 four dimensinal theories. In the Nf = NC − 1 case, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N =2 four dimensional theory. The decompactification limit of the superpotential for pure g...

A topological approach to quark fractional charges, based on charge constraints unexplained by the Standard Model of particle physics, is discussed. Charge fractionalization is related to a tunneling process occurring in time between pure gauge field configurations at the far past and future associated with integer-charged bare quarks, named prequarks. This transition conforms to a topologicall...

Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. In this talk I discuss the interpretation of these Monte Carlo results in terms of our cu...

We have constructed the lowest few eigenvectors of the staggered Dirac operator on SU (3) gauge configurations, both quenched and dynamical. We use these modes to study the topological charge and to construct approximate hadronic correlators.

We present preliminary results for a high statistics study of the topological charge distribution in the SU(3) Yang-Mills theory obtained by using the definition of the charge suggested by Neu-berger fermions. We find statistical evidence for deviations from a gaussian distribution. The large statistics required has been obtained by using PCs of the INFN-GRID.