Connes' gauge theory is defined on noncommutative space-times. It is applied to formulate a noncommutative Glashow-Weinberg-Salam (GWS) model in the leptonic sector. It is shown that the model has two Higgs doublets and the gauge bosons sector after the Higgs mechanism contains the massive charged gauge fields, two massless and two massive neutral gauge fields. It is also shown that, in the tre...

In previous work [Rosenbaum M. et al., we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutati-vity. However, fo...

Existence and uniqueness of the solution are proved for the ‘master equation’ derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with NF charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V -equivalence relation for the gauge ...

We present a gauge independent Lagrangian method of abstracting the reduced space of a solvable model with Gribov-like ambiguity, recently proposed by Friedberg, Lee, Pang and Ren. The reduced space is found to agree with the explicit solutions obtained by these authors. Complications related to gauge fixing are analysed. The Gribov ambiguity manifests by a nonuniqueness in the canonical transf...

We solve the Gauss law of SU(2) lattice gauge theory using the harmonic oscillator prepotential formulation. We construct a generating function of a manifestly gauge invariant and orthonormal basis in the physical Hilbert space of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal physical states are given in closed form. The generalization to SU(N) gauge group is discussed.

We consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space, pointing out features related to dimensional transmuta...

We present a Liouville-string approach to confinement in four-dimensional gauge theories, which extends previous approaches to include non-conformal theories. We consider Liouville field theory on world sheets whose boundaries are the Wilson loops of gauge theory, which exhibit vortex and spike defects. We show that world-sheet vortex condensation occurs when the Wilson loop is embedded in four...

A very simple field theory in noncommutative phase space (X M , P M) in d + 2 dimensions , with a gauge symmetry based on noncommutative u ⋆ (1, 1), furnishes the foundation for the field theoretic formulation of Two-Time Physics. This leads to a remarkable unification of several gauge principles in d dimensions, including Maxwell, Einstein and high spin gauge principles, packaged together into...

We show that noncommutative U(r) gauge theories with a chiral fermion in the adjoint representation can be constructed on the lattice with manifest star-gauge invariance in arbitrary even dimensions. Chiral fermions are implemented using a Dirac operator which satisfies the Ginsparg-Wilson relation. A gauge-invariant integration measure for the fermion fields can be given explicitly, which simp...

We find a new Penrose limit of AdS5 × S5 that gives the maximally symmetric pp-wave background of Type IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N = 4 SYM theory. The new Penrose limit, when applied to AdS5×S/ZM , yields a pp-wave with a space-...