Effective Abelian Theory Research Articles

Issues in topological gauge theory

We discuss topological theories, arising from the general N = 2 twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of sources and study the mixing between the various p-observables. We present the twisted superfield formalism which makes duality transformations transparent. We propose a scheme which uniquely fixes all the contact terms. We derive a formula for the correlation functions of p-observables on the manifolds of generalized simple type for 0 ⪕ p ⪕ 4 and on some manifolds with b 2 + = 1. We study the theories with matter and explore the properties of universal instantons. We also discuss the compactifications of higher dimensional theories. Some relations to sigma models of type A and B are pointed out and exploited.

Ward identities for Yang-Mills theory in Abelian gauges: Abelian dominance at high energies

We consider Yang-Mills theory in a general class of Abelian gauges. Exploiting the residual Abelian symmetry on a quantum level, we derive a set of Ward identities in functional form, valid to all orders in perturbation theory. As a consequence, the coupling constant is only renormalised through the Abelian two-point function. This implies that asymptotic freedom in all Abelian gauges can be understood from an effective Abelian theory alone, which can be interpreted as Abelian dominance in the high energy regime.

Scaling and confinement aspects of tadpole-improved SU(2) lattice gauge theory and its Abelian projection

Using a tadpole improved SU(2) gluodynamics action, the nonabelian potential and the abelian potential after the abelian projection are computed. Rotational invariance is found restored at coarse lattices both in the nonabelian theory and in the effective abelian theory resulting from maximal abelian projection. Asymptotic scaling is tested for the SU(2) string tension. Deviation of the order of $6%$ is found, for lattice spacings between 0.27 and 0.06 fm. Evidence for asymptotic scaling and scaling of the monopole density in maximal abelian projection is also seen, but not at coarse lattices. The scaling behavior is compared with analyses of Wilson action results, using bare and renormalized coupling schemes. Using extended monopoles, evidence is found that the gauge dependence of the abelian projection reflects short distance fluctuations, and may thus disappear at large scales.

Dual superconductivity in the SU(2) pure gauge vacuum: A lattice study.

We investigate the dual superconductivity hypothesis in pure SU(2) lattice gauge theory. We focus on the dual Meissner effect by analyzing the distribution of the color fields due to a static quark-antiquark pair. We find evidence of the dual Meissner effect both in the maximally Abelian gauge and without gauge fixing. We measure the London penetration length. Our results suggest that the London penetration length is a physical gauge-invariant quantity. We put out a simple relation between the penetration length and the square root of the string tension. We find that our extimation is quite close to the extrapolated continuum limit available in the literature. A remarkable consequence of our study is that an effective Abelian theory can account for the long range properties of the SU(2) confining vacuum.