Supersymmetric Yang-Mills quantum mechanics in various dimensions

Recent analytical and numerical solutions of the above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting continuous and discrete spectra in the four-dimensional system, together with the identification of dynamical supermultiplets and SUSY vacua. New construction of the gluinoless SO(9) singlet state, which is vastly different from the empty state, in the ten-dimensional model is also briefly summarized.Comment: Talk presented at the Eighth Workshop on Non-Perturbative QCD, Paris, June 2004; 8 pages, 4 figure

Exact Witten Index in D=2 supersymmetric Yang-Mills quantum mechanics

A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides the spectrum and restricted Witten index of the system with very high precision (taking into account up to $10^5$ quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time.Comment: 13 pages, 1 figur

Calorons on the lattice - a new perspective

We discuss the manifestation of instanton and monopole solutions on a periodic lattice at finite temperature and their relation to the infinite volume analytic caloron solutions with asymptotic non-trivial Polyakov loops. As a tool we use improved cooling and twisted boundary conditions. Typically we find 2Q lumps for topological charge Q. These lumps are BPS monopoles.Comment: Latex. 16 pages, 9 figure

Non perturbative determination of the running coupling constant in quenched SU(2)

Through a finite size renormalization group technique we calculate the running coupling constant for quenched SU(2) with a few percent error over a range of energy varying by a factor thirty. The definition is based on ratio of correlations of Polyakov loops with twisted boundary conditions. The extrapolation to the continuum limit is governed by corrections due to lattice artifacts which are proportional to the square of the lattice spacing and appears rather smooth.Comment: 18 pages of ps fil

Recent results on self-dual configurations on the torus

We review the recent progress on our understanding of self-dual SU(N) Yang-Mills configurations on the torus.Comment: Latex 3 pages, 1 figure. Contribution to the Lat99 Proceeding

On the stability of Dirac sheet configurations

Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic field configurations were left over after the annihilation of constituents that formed metastable Q=0 configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently non-trivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations

Genetic and Environmental Influences on the Development of Intelligence

Measures of intelligence were collected in 209 twin pairs at 5, 7, 10, and 12 years of age, as part of a longitudinal project on intelligence, brain function, and behavioral problems. Intelligence was measured at 5, 7, and 10 years of age with the RAKIT, a well-known Dutch intelligence test, consisting of 6 subscales. At 12 years of age, the complete WISC-R was administered (12 subscales). Both intelligence tests resulted in a measure of full-scale IQ (FSIQ). Participation rate is around 93% at age 12. Correlation coefficients over time are high: (r(5-7) = .65; r(5-10) = .65; r(5-12) = .64; r(7-10) = .72; r(7-12) = .69 and r(10-12) = .78). Genetic analyses show significant heritabilities at all ages, with the expected increase of genetic influences and decrease of shared environmental influences over the years. Genetic influences seem to be the main driving force behind continuity in general cognitive ability, represented by a common factor influencing FSIQ at all ages. Shared environmental influences are responsible for stability as well as change in the development of cognitive abilities, represented by a common factor influencing FSIQ at all ages and age-specific influences, respectively

Heritability of educational achievement in 12-year olds and the overlap with cognitive ability

In order to determine high school entrance level in the Netherlands, nowadays, much value is attached to the results of a national test of educational achievement (CITO), administered around age 12. Surprisingly, up until now, no attention has been paid to the etiology of individual differences in the results of this national test of educational achievement. No attempt has been made to address the question about the nature of a possible association between the results of the CITO and cognitive abilities, as measured by psychometric IQ. The aim of this study is to explore to what extent psychometric IQ and scholastic achievement, as assessed by the CITO high school entrance test, are correlated. In addition, it was investigated whether this expected correlation was due to a common genetic background, shared or nonshared environmental influences common to CITO and intelligence or a combination of these influences. To this end multivariate behavior genetic analyses with CITO and IQ at ages 5, 7, 10 and 12 years have been conducted. The correlations were .41, .50, .60, and .63 between CITO and IQ assessed at age 5, 7, 10, and 12 respectively. The results of the analyses pointed to genetic effects as the main source of variance in CITO and an important source of covariance between CITO and IQ. Additive genetic effects accounted for 60% of the individual differences found in CITO scores in a large sample of Dutch 12-year-olds. This high heritability indicated that the CITO might be a valuable instrument to assess individual differences in cognitive abilities in children but might not be the right instrument to put the effect of education to the test