We introduce the self-dual abelian gauged O(3) sigma models where the Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge field. These models have quite rich structures and various limits. Our models are found to exhibit both symmetric and broken phases of the gauge group.We discuss the pure Chern-Simons limit in some detail and study rotationally symmetric solitons. PACS number(s):

The latest MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss three different ways to estimate the mass of the electroweak monopole. We first present the dimensional and scaling arguments which indicate the monopole mass to be around 4 to 10 TeV . To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strength at short distance. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC.

We study global vortices coupled to (2+1) dimensional gravity with negative cosmological constant. We found nonsingular vortex solutions in φ 4 -theory with a broken U(1) symmetry, of which the spacetimes do not involve physical curvature singularity. When the magnitude of negative cosmological constant is larger than a critical value at a given symmetry breaking scale, the spacetime structure is a regular hyperbola, however it becomes a charged black hole when the magnitude of cosmological constant is less than the critical value. We explain through duality transformation the reason why static global vortex which is electrically neutral forms black hole with electric charge. Under the present experimental bound of the cosmological constant, implications on cosmology as a straight black cosmic string is also discussed in comparison with global U(1) cosmic string in the spacetime of the zero cosmological constant.

We present two independent methods to estimate the mass of the electroweak monopole. Our result strongly implies the existence of a genuine electroweak monopole of mass around 4 to 10 TeV, which could be detected by MoEDAL at present LHC. We emphasize that the discovery of the the electroweak monopole should be the final test of the standard model.PACS numbers: PACS Number(s): 14.80. Hv, 11.15.Tk, 02.40.+m The recent "discovery" of Higgs particle at LHC has reconfirmed that the standard model describes the real world [1]. Indeed it has been interpreted that the standard model has passed the "final" test with the discovery. But we emphasize tha the final test of the standard model should come from the discovery of the electroweak ("Cho-Maison") monopole, because the theory predicts the electroweak monopole [2,3]. It has the monopole topology, and naturally accommodates the Cho-Maison monopole as the electroweak generalization of the Dirac's monopole [4].Ever since Dirac predicted the existence of the monopole, the monopole has been an obsession [5][6][7][8][9]. The Abelian monopole has been generalized to the nonAbelian monopoles by Wu and Yang [5,6] who showed that the pure SU (2) gauge theory allows a point-like monopole, and by 't Hooft and Polyakov [7,8] who have constructed a finite energy monopole solution in GeorgiGlashow model as a topological soliton. Moreover, the monopole in grand unification has been constructed by Dokos and Tomaras [9].But it has been asserted that the Weinberg-Salam model has no topological monopole of physical interest [10]. The basis for this "non-existence theorem" is that the quotient space SU (2) × U (1)/U (1) em allows no non-trivial second homotopy which can accommodate the monopole.This claim, however, is unfounded [2,3]. This is because the Weinberg-Salam model, with the hypercharge U (1) Y , could be viewed as a gauged CP 1 model in which the (normalized) Higgs doublet plays the role of the CP 1 field. So, if the standard model is correct, the electroweak monopole must exist. This makes the experimental detection of the electroweak monopole an urgent matter.Fortunately the latest MoEDAL detector ("The Magnificient Seventh") at LHC is actively searching for such * Electronic address: ymcho7@konkuk.ac.kr monopole [11]. To help the experiment discover the monopole, however, we need a theoretical estimate of the monopole mass. The purpose of this Letter is to estimate the mass of the electroweak monopole to be around 4 to 10 TeV.The importance of the electroweak monopole is twofold. First, it is the straightforward and natural generalization of the Dirac monopole to the electroweak theory which is unavoidable when the electrodynamics is unified to the electroweak theory. This means that the monopole which should exist in the real world is not likely to be the Dirac monopole but this one.Second, unlike the Dirac monopole which is optional, the electroweak monopole must exist because the standard model has the monopole topology. This means that the final test of the standard ...

Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π 3 (S 3 ) and the monopole topology π 2 (S 2 ). With this we propose to classify the skyrmions by two topological numbers (m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the (m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B = mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the SineGordon theory and QCD combined together, which can also be classified by two topological numbers ( p, q). This puts the Skyrme theory in a totally new perspective.