Deformations of the embedding of the SU(2) monopole solution in SU (3)

This paper is concerned with static Yang-Mills-Higgs fields, in the Prasad-Sommerfield limit of no Higgs self-interaction. One can obtain SU (3) multipole solutions from SU(2) solutions by embedding, in several different ways. In some of these cases, the embedding belongs to a family of SU(3) solutions that are not all embeddings; in other words, some embeddings can be deformed into non-embeddings. The simplest case, an embedding of the SU(2) spherically symmetric monopole, is studied with the aid of the twistor construction procedure. The family of axially symmetric SU(3) solutions to which it belongs is described.     

A Schwarzschild-like model for baryons

We present a toy model of baryons using singular solutions of the SU(2) Yang-Mill-Higgs (YMH) field equations, which bears some similarity to the Schwarzschild solution of general relativity. The SU (2) solutions are used as a background field into which a scalar, SU (2) test particle is placed. This can be compared to placing an electrically charged particle in a Coulomb background field, except the SU (2) YMH solutions are singular on a spherical membrane thus trapping (confining) the test particle inside the sphere in a manner similar to certain bag models of baryons. An interesting consequence of this model is that the composite system is a fermion even though the original Lagrangian contains only bosonic fields.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Triplication of SU(5) Monopoles

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5)-->[SU(3) x SU(2) x U(1)]/Z(3) x Z(2) symmetry breaking. We find that there are three solutions that are gauge equivalent but, as we argue, would correspond to physically distinct degrees of freedom in the dualized version of the model. The triplication of monopoles could help us understand the observed family structure of standard model particles.     

Magnetic monopoles in SU(3) and SU(2) gauge theories without Higgs' scalars

We show that certain known singular solutions for pure SU(3) Yang-Mills theory carry magnetic charges with respect to both U(1) subgroups of SU(3). A topological characterisation in terms of monopoles is given to the SU(2) singular solutions of Wu and Yang.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

An approach to SU(2) gauge fields in Minkowski space-time

A reparametrization-invariant formulation of SU(2) gauge theory in Minkowski space-time is given in terms of differential forms. A map of space-time into a compact region is used and the SU(2) Maurer-Cartan forms employed to establish a convenient gauge. New solutions to the theory are presented and discussed.     

Gravitating Dyons and Dyonic Black Holes in SU(2) and SU(5) Theories

The study of gravitating dyons and dyonic black holes in SU(2) and SU(5) theories has been undertaken and it has been shown that gravitating fundamental dyonic solutions and dyonic black holes are stable in both the cases.     

Squeezed Number State Solutions of Generalized Two-Mode Harmonic Oscillators Model： an Algebraic Approach

Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2) squeezed number states respectively. Some statistical properties of these states are also discussed.     

Squeezed Number State Solutions of Generalized Two-Mode Harmonic Oscillators Model:an Algebraic Approach

Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.     

New exact solutions of the Yang-Mills field equations

In this paper new exact solutions of the Yang-Mills SU(2) gauge field equations are obtained using the Carmeli-Charach-Kaye null-tetrad formalism. The solutions are classified and briefly discussed.     

Non selfdual complex solutions with finite,complex euclidean actions for SU(2) Yang-Mills fields

A pair of complex conjugate solutions are presented for classical SU(2) gauge fields in four-dimensional flat euclidean space. The solutions are non selfdual and have finite complex actions.     

On Spin(7) holonomy metric based on SU(3)/U(1): II

We continue the investigation of Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A special choice of U(1) embedding in SU(3) allows more general metric ansatz with five metric functions. There are two possible singular orbits in the first-order system of Spin(7) instanton equation. One is the flag manifold SU(3)/T² also known as the twistor space of CP(2) and the other is CP(2) itself. Imposing a set of algebraic constraints, we find a two-parameter family of exact solutions which have SU(4) holonomy and are asymptotically conical. There are two types of asymptotically locally conical (ALC) metrics in our model, which are distinguished by the choice of S¹ circle whose radius stabilizes at infinity. We show that this choice of M theory circle selects one of the possible singular orbits mentioned above. Numerical analyses of solutions near the singular orbit and in the asymptotic region support the existence of two families of ALC Spin(7) metrics: one family consists of deformations of the Calabi hyper-Kähler metric, the other is a new family of metrics on a line bundle over the twistor space of CP(2).     

Lorentz-invariant solutions of the classical Yang-Mills equations

A gauge representation of the noncompact group SL(2,C) is defined. All the corresponding invariant (singular) solutions of the classical Yang-Mills equations in Minkowski space are found. It is shown that they are related to a family of real SU(2) x SU(2)-invariant Euclidean solutions containing the self-dual (one-instanton) configurations.     

Non-abelian traveling wave solutions for massless QCD2

The field equations for quantum chromodynamics in 1 + 1 dimensions (QCD₂) with massless fermions are shown to admit classical non-abelian traveling wave solutions. In this case, the field equations reduce to the linear Frenet-Serret equations for a curve in the three-space corresponding to an SU(2) subalgebra of the SU(N) gauge group.     

SU(2)-multi-instantons over S 2×S 2

Making use of the general theory of connections invariant under a symmetry group which acts transitively on fibers, explicit solutions are derived for SU(2)×SU(2)-symmetric multi-instantons over S ²×S ², with SU(2) structure group. These multi-instantons correspond to a principal fiber bundle characterized by a second Chern number given by 2m ², with m an integer.     

Stationary and periodic regimes in relaxing media with fluctuations

The non-linear Kerr medium in the presence of damping and earlier associated with an SU(1,1) symmetry, is exactly solved as a spin damped system, associated with an SU(2) symmetry. The association with SU(2) is exploited to express the dynamics of the system as a Schrödinger-like equation, whose solution is obtained using the appropriate disentanglement theorem. This method is then extended to multi-mode coupled nonlinear oscillators for obtaining exact solutions.     

Chern-Simons solitons,Toda theories and the chiral model

The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)-dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge dynamics. In this paper we classify all finite chargeSU(N) solutions by first transforming the self-dual Chern-Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck-Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between theSU(N) Toda andSU(N) chiral model solutions.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069, and NSF grant #87-08447     

Low energy static Yang-Mills configurations

Non-singular static solutions for the SU(2) Yang-Mills field equations in the presence of external sources are presented. These solutions possess energies less than those of the magnetic dipole solutions, and can in fact have vanishingly small energies.     

Exact Solutions for Self-Dual SU(2) and SU(3) Yang–Mills Fields

The (constrained) canonical reduction of four-dimensional self-dual SU(2) and SU(3) Yang–Mills theory to two-dimensional nonlinear Schrödinger (NS) and Korteweg–de Vries (KdV) equations are considered. The Bäcklund transformations (BTs) are implemented to obtain new classes of exact solutions for the reduced two-dimensional NS and KdV models.