There is a Nahm transform for two-dimensional gauge fields which establishes a one-to-one correspondence between the orbit space of U (N) gauge fields with topological charge k defined on a torus and that of U (k) gauge fields with charge N on the dual torus. The main result of this paper is to show that a similar duality transform cannot exist for CP N instantons. This fact establishes a signi...

We review recent results on solitons in supersymmetric (SUSY) non-Abelian gauge theories, focusing on our papers: hep-th/0405194, hep-th/0405161, and hep-th/0404198. We construct the BPS multi-wall solutions in supersymmetric U(NC) gauge theories in five dimensions with NF(> NC) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite...

Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables. Physically the restriction to compact gauge group is enough for the study of Yang-mills theories, however it is well known that non-compact groups naturally ari...

We investigate the structure of the configuration space of gauge theories and its description in terms of the set of absolute minima of certain Morse functions on the gauge orbits. The set of absolute minima that is obtained when the background connection is a pure gauge is shown to be isomorphic to the orbit space of the pointed gauge group. We also show that the stratum of irreducible orbits ...

This is the second paper concerning gauge-invariant coherent states for Loop Quantum Gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the abelian U(1) case encountered in the previous article. We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss-peaked in ga...

We construct a twistor space action for N = 4 super Yang-Mills theory and show that it is equivalent to its four dimensional spacetime counterpart at the level of perturbation theory. We compare our partition function to the original twistor-string proposal, showing that although our theory is closely related to string theory, it is free from conformal supergravity. We also provide twistor acti...

The study of physics beyond 4-dimensional (4D) space-time traces back to the work by Kaluza and Klein. 1) The exsitence of an extra space is essential in superstring theory 2), 3) and M -theory. 4) Recently, there is a lot of interesting research of the phenomenological and theoretical implications of an extra space with large radii based on several motivations. 5) As a feature in theories with...

A noncommutative gauge theory can be realized by considering branes in string theory with a constant NeveuSchwarz–Neveu-Schwarz ~NS-NS! two-form field @1#. In @2#, it was shown that there are two equivalent descriptions of the theory: one in terms of ordinary gauge fields Ai on a commutative space and another in terms of noncommutative gauge fields  i on a noncommutative space whose coordinate...

The transverse lattice 1 is an attempt to combine advantages of the light-front (LF) and lattice formulations of QCD. In this approach to QCD the time and one space direction (say x) are kept continuous, while the two ‘transverse’ directions x⊥ ≡ (x , x) are discretized. Keeping the time and x directions continuous has the advantage of preserving manifest boost invariance for boosts in the x di...

We study the moduli space of M -theories compactified on G2 manifolds which are asymptotic to a cone over quotients of S × S. We show that the moduli space is composed of several components, each of which interpolates smoothly among various classical limits corresponding to low energy gauge theories with a given number of massless U(1) factors. Each component smoothly interpolates among supersy...