Integrability and supersymmetry of the supersymmetric extension of the sine-Gordon theory on a half-line are examined and the boundary potential which preserves both the integrability and supersymmetry on the bulk is derived. It appears that unlike the boundary bosonic sine-Gordon theory, integrability and supersymmetry strongly restrict the form and… (More)
We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in… (More)
We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the… (More)
We construct a generalization of the two-dimensional Wess-Zumino-Witten model on a 2n-dimensional Kähler manifold as a group-valued non-linear sigma model with an anomaly term containing the Kähler form. The model is shown to have an infinite-dimensional symmetry which generates an n-toroidal Lie algebra. The classical equation of motion turns out to be the… (More)
Nonlinear sigma models (NLSM) in d = 3 have many interesting and non-trivial features, which were explored poorly in contrast with NLSM in d = 2 and d = 4. We present a few results from our study of the perturbative and non-pertubative properties of three-dimensional (3D) NLSM. i) We have shown that cancellation of ultraviolet (UV) divergences takes place… (More)
We find non-BPS solutions of the noncommutative CP 1 model in 2+1 dimensions. These solutions correspond to soliton anti-soliton configurations. We show that the one-soliton one-anti-soliton solution is unstable when the distance between the soliton and the anti-soliton is small. We also construct time-dependent solutions and other types of solutions.
We construct a closed form of the action of the supersymmetric CP N sigma model on noncommutative superspace in four dimensions. We show that this model has N = 1 2 supersymmetry and that the transformation law is not modified. The supersymmetric CP N sigma model on noncommutative superspace in two dimensions is obtained by dimensional reducing the model in… (More)
We have evaluated by numerical simulation the average size R(K) of random polygons of fixed knot topology K=,3(1),3(1) musical sharp 4(1), and we have confirmed the scaling law R(2)(K) approximately N(2nu(K)) for the number N of polygonal nodes in a wide range; N=100-2200. The best fit gives 2nu(K) approximately 1.11-1.16 with good fitting curves in the… (More)
We construct noncommutative extension of the Wess-Zumino-Witten (WZW) model and study its ultraviolet property. The β-function of the U (N) noncom-mutative WZW model resembles that of the ordinary WZW model. The U (1) noncommutative model has also a nontrivial fixed point.
We investigate the structure of an infinite-dimensional symmetry of the four-dimensional Kähler WZW model, which is a possible extension of the two-dimensional WZW model. We consider the SL(2, R) group and, using the Gauss decomposition method, we derive a current algebra identified with a two-toroidal Lie algebra, a generalization of the affine Kac-Moody… (More)