Dirac's Observables for the SU(3)XSU(2)XU(1) Standard Model

The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1) model with Grassmann-valued fermion fields in the Higgs phase is given. We bypass the complications of the Hamiltonian theory in the Higgs phase, resulting from the spontaneous symmetry breaking with the Higgs mechanism, by studying the Hamiltonian formulation of the Higgs phase for the gauge equivalent Lagrangian in the unitary gauge. A canonical basis of Dirac's observables is found and the reduced physical Hamiltonian is evaluated. Its self-energy part is nonlocal for the electromagnetic and strong interactions, but local for the weak ones. Therefore, the Fermi 4-fermion interaction reappears at the nonperturbative level.Comment: 90 pages, RevTeX, no figure

Self-Dual Chern-Simons Solitons in (2+1)-Dimensional Einstein Gravity

We consider here a generalization of the Abelian Higgs model in curved space, by adding a Chern--Simons term. The static equations are self-dual provided we choose a suitable potential. The solutions give a self-dual Maxwell--Chern--Simons soliton that possesses a mass and a spin

Vortices in Bogomol'nyi Limit of Einstein Maxwell Higgs Theory with or without External Sources

The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol'nyi-type bound. We examine cylindrically symmetric solutions to Einstein equations and the first-order Bogomol'nyi equations, and find vortex solutions and vortex-particle composites which lie on the spatial manifold with global geometry described by a cylinder asymptotically or a two sphere in addition to the well-known cone.Comment: LaTeX, 23 pages, 10 LaTeX figures included, KHTP-93-05, SNUTP-93-100, DPNU-93-46. (A note and several references added

Bogomolnyi Bound with a Cosmological Constant

Bogomolnyi-type bound is constructed for the topological solitons in O(3) nonlinear $\sigma$ model coupled to gravity with a negative cosmological constant. Spacetimes made by self-dual solutions form a class of G\"{o}del-type universe. In the limit of a spinless massive point particle, the obtained stationary metric does not violate the causality and it is a new point particle solution different from the known static hyperboloid and black hole. We also showed that static Nielsen-Olesen vortices saturate Bogomolnyi-type bound only when the cosmological constant vanishes.Comment: 11 pages, RevTe

Gravitating Chern-Simons vortices

The construction of self-dual vortex solutions to the Chern-Simons-Higgs model (with a suitable eighth-order potential) coupled to Einstein gravity in (2 + 1) dimensions is reconsidered. We show that the self-duality condition may be derived from the sole assumption $g_{00} = 1$. Next, we derive a family of exact, doubly self-dual vortex solutions, which interpolate between the symmetrical and asymmetrical vacua. The corresponding spacetimes have two regions at spatial infinity. The eighth-order Higgs potential is positive definite, and closed timelike curves are absent, if the gravitational constant is chosen to be negative.Comment: 11 pages, LaTe

Chern-Simons Vortices in Supergravity

We study supersymmetric vortex solutions in three-dimensional abelian gauged supergravity. First, we construct the general U(1)-gauged D=3, N=2 supergravity whose scalar sector is an arbitrary Kahler manifold with U(1) isometry. This construction clarifies the connection between local supersymmetry and the specific forms of some scalar potentials previously found in the literature -- in particular, it provides the locally supersymmetric embedding of the abelian Chern-Simons Higgs model. We show that the Killing spinor equations admit rotationally symmetric vortex solutions with asymptotically conical geometry which preserve half of the supersymmetry.Comment: 26 pages, LaTeX2

Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.Comment: 25 pages; ref added; to appear in J. Phys.

Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory

We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer $k$ which appears in the extended ADHM construction should be interpreted as the $D4$-brane charge rather than the $D0$-brane charge by explicitly calculating the topological charges in the case that the noncommutativity parameter is anti-self-dual. We also find the relationship with the solution generating technique and show that the integer $k$ can be interpreted as the charge of the $D0$-brane bound to the $D8$-brane with the $B$-field in the case that the noncommutativity parameter is self-dual.Comment: 22 page

Global Vortex and Black Cosmic String

We study global vortices coupled to (2+1) dimensional gravity with negative cosmological constant. We found nonsingular vortex solutions in $\phi^4$-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.Comment: 35 pages, Late

On S-duality in (2+1)-Chern-Simons Supergravity

Strong/weak coupling duality in Chern-Simons supergravity is studied. It is argued that this duality can be regarded as an example of superduality. The use of supergroup techniques for the description of Chern-Simons supergravity greatly facilitates the analysis.Comment: 10+1 pages, latex, no figure