Decay of pseudoscalars into lepton pairs and large-Nc QCD

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colours Nc. When further restricted to the lowest meson dominance approximation to large-Nc QCD, our results agree well with the available experimental data.Comment: 5 pages, 2 figure

On the relevance of center vortices to QCD

In a numerical experiment, we remove center vortices from an ensemble of lattice SU(2) gauge configurations. This removal adds short-range disorder. Nevertheless, we observe long-range order in the modified ensemble: confinement is lost and chiral symmetry is restored (together with trivial topology), proving that center vortices are responsible for both phenomena. As for the Abelian monopoles, they survive but their percolation properties are lost.Comment: 4 pages, 5 figures; discussion expanded, text compressed... to appear in Phys. Rev. Let

A Systematic Extended Iterative Solution for QCD

An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while allowing renormalization by the perturbative counterterms. Proper vertices Gamma are approximated by a double sequence Gamma[r,p], with r the degree of rational approximation w.r.t. the QCD mass scale Lambda, nonanalytic in the coupling g, and p the order of perturbative corrections in g-squared, calculated from Gamma[r,0] - rather than from the perturbative Feynman rules Gamma(0)(pert) - as a starting point. The mechanism allowing the nonperturbative terms to reproduce themselves in the Dyson-Schwinger equations preserves perturbative renormalizability and is tied to the divergence structure of the theory. As a result, it restricts the self-consistency problem for the Gamma[r,0] rigorously - i.e. without decoupling approximations - to the superficially divergent vertices. An interesting aspect of the scheme is that rational-function sequences for the propagators allow subsequences describing short-lived excitations. The method is calculational, in that it allows known techniques of loop computation to be used while dealing with integrands of truly nonperturbative content.Comment: 48 pages (figures included). Scope of replacement: correction of a technical defect; no changes in conten

The Finiteness Requirement for Six-Dimensional Euclidean Einstein Gravity

The finiteness requirement for Euclidean Einstein gravity is shown to be so stringent that only the flat metric is allowed. We examine counterterms in 4D and 6D Ricci-flat manifolds from general invariance arguments.Comment: 15 pages, Introduction is improved, many figures(eps

THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL

Using the exact path integral solution of the Schwinger model -- a model where instantons are present -- the Dyson-Schwinger equation is shown to hold by explicit computation. It turns out that the Dyson-Schwinger equation separately holds for every instanton sector. This is due to Theta-invariance of the Schwinger model.Comment: LATEX file 11 pages, no figure

Entanglement entropy in lattice gauge theories

We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way. In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions. Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology. This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the simplest example of Z2 lattice gauge theory in (2 + 1) dimensions we demonstrate the relation between entanglement entropy and the classical entropy of the field flux. For SU(2) lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region. We also comment on the holographic interpretation of the entanglement entropy.Comment: Talk presented at the Confinement8 conference (Mainz, Germany, September 1 - 6, 2008) and at the conference "Liouville Field Theory and Statistical Models", dedicated to Alexey Zamolodchikov memory (Moscow, Russia, June 21 - 24, 2008

Dual Superconductivity. Variations on a Theme

It is pointed out that the low energy effective theory that describes the low lying glueballs of the pure Yang Mills theory sustains static classical stringlike solutions. We suggest that these objects can be identified with the QCD flux tubes and their energy per unit length with the string tension.Comment: 14 pages, latex, no figures, to be published in the special issue of Foundations of Physics dedicated to Larry Horwit

Thermal duality and gravitational collapse

Thermal duality is a relationship between the behaviour of het-erotic string models of the E(8)xE(8) or SO(32) types at inversely related temperatures, a variant of T duality in the Euclidean regime. This duality would have consequences for the nature of the Hagedorn transition in these string models. We propose that the vacuum admits a family of deformations in situations where there are closed surfaces of constant area but high radial acceleration (a string regularized ver-sion of a Penrose trapped surface), such as would be formed in situ-ations of extreme gravitational collapse. This would allow a radical resolution of the firewall paradox by allowing quantum effects to sig-nificantly modify the spacetime geometry around a collapsed object. A string bremsstrahlung process would convert the kinetic energy of infalling matter in extreme gravitational collapse to form a region of the deformed vacuum, which would be equivalent to forming a high temperature string phase. A heuristic criterion for the conversion pro-cess is presented, relating Newtonian gravity to the string tension, suggesting an upper limit to the strength of the gravitational interac-tion. This conversion process might have observable consequences for charged particles falling into a rotating collapsed object by producing high energy particles via a variant of the Penrose process

Gravity on de-Sitter 3-Brane, Induced Einstein-Hilbert Term and Massless Gravitons

We study the extensions of DGP model which are described by five-dimensional Einstein gravity coupled covariantly to 3-brane with induced gravity term and consider warped D=4 de Sitter background field solutions on the brane. The case with included D=5 AdS cosmological term is also considered. Following background field method we obtain the field equations described by the Lagrangean terms bilinear in gravitational field. In such a linear field approximation on curved dS background we calculate explicitly the five-dimensional massive terms as well as the mass-like ones on the brane. We investigate the eigenvalue problem of Schr\"{o}dinger-like equation in fifth dimension for graviton masses and discuss the existence of massless as well as massive graviton modes in the bulk and on the brane without and with induced gravity.Comment: LaTeX 26 pages, the version which appears in Class. Quant. Gra

Eta' Mass and Chiral Symmetry Breaking at Large Nc and Nf

We propose a method for implementing the large-Nc, large-Nf limit of QCD at the effective Lagrangian level. Depending on the value of the ratio Nf/Nc, different patterns of chiral symmetry breaking can arise, leading in particular to different behaviors of the eta-prime mass in the combined large-N limit.Comment: revtex 12 pages, one postscript figur