Using the results of several quenched lattice simulations, we predict the value of the strange and charm quark masses in the continuum at the next-to-leading order, m M S s (µ = 2 GeV) = (128 ± 18) MeV and m M S ch (µ = 2 GeV) = (1.48± 0.28) GeV. The errors quoted above have been estimated by taking into account the original statistical error of the lattice results and the uncertainties coming ...

We study the one–loop renormalization of noncommutative U (N) gauge theories without matter. We find that for N > 1 the renormalization of the four-point function requires a counterterm which is not present in ordinary gauge theories and breaks the noncommutative gauge invariance. This counterterm is reminiscent of a nonplanar contribution in string theory.

The entanglement entropy of SU(N) lattice gauge theory is studied exactly in 1 + 1 space-time dimensions and in Migdal-Kadanoff approximation in higher dimensional space. The existence of a non-analytical behavior reminiscent of a phase transition for a characteristic size of the entangled region is demonstrated for higher dimensional theories.

The three dimensional U(1) Lattice Gauge, in the weak coupling limit, is dual to a Discrete Gaussian model. We investigate this dual model and use it to calculate properties of the U(1) theory. We find that, because of the nature of the dual model, its advantages are outweighed by large autocorrelation times generated when the dual system becomes disordered.

Chern-Simons theory is analyzed with a gauge-fixing which allows to discuss the Landau gauge and the light-cone gauge at the same time.

Declaration I state that the work embodied in this thesis forms my own contribution to the research work carried out under the guidance of Prof. Rajiv V. Gavai. This work has not been submitted for any other degree to this or any other University or body. Whenever references have been made to previous works of others, it has been clearly indicated. (signature of the supervisor) (signature of th...

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at N = ∞ for arbitrary dimension D. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows as φ α where α = 1 +

First results of a non–singlet QCD analysis of the structure function F2(x,Q ) in 3–loop order based on the non– singlet world data are presented. Correlated errors are determined and their propagation through the evolution equations is performed analytically. The value for αs(MZ) is determined to be 0.1135 + / − 0.0023/0.0026 compatible with results from other QCD analyses. Low moments for uv(...

We investigate SU(2) lattice gauge theory in four dimensions in the maximally abelian projection. Studying the effects on different lattice sizes we show that the deconfinement transition of the fields and the percolation transition of the monopole currents in the three space dimensions are precisely related. To arrive properly at this result the uses of a mathematically sound characterization ...

We construct lattice actions for a variety of (2, 2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.