Dynamics of CP^1 lumps on a cylinder

The slow dynamics of topological solitons in the CP^1 sigma-model, known as lumps, can be approximated by the geodesic flow of the L^2 metric on certain moduli spaces of holomorphic maps. In the present work, we consider the dynamics of lumps on an infinite flat cylinder, and we show that in this case the approximation can be formulated naturally in terms of regular Kaehler metrics. We prove that these metrics are incomplete exactly in the multilump (interacting) case. The metric for two-lumps can be computed in closed form on certain totally geodesic submanifolds using elliptic integrals; particular geodesics are determined and discussed in terms of the dynamics of interacting lumps.Comment: 35 pages, 10 figure

Gauged vortices in a background

We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class of the abelian Higgs model approximately truncates to a finite-dimensional moduli space with a Kaehler structure. For the case where the vortices live on a 2-sphere, we explain how localisation formulas on the moduli spaces can be used to compute explicitly the partition function of the vortex gas interacting with a background potential. The coefficients of this analytic function provide geometrical data about the Kaehler structures, the simplest of which being their symplectic volume (computed previously by Manton using an alternative argument). We use the partition function to deduce simple results on the thermodynamics of the vortex system; in particular, the average height on the sphere is computed and provides an interesting effective picture of the ground state.Comment: Final version: 22 pages, LaTeX, 1 eps figur

Wage mobility, Job mobility and Spatial mobility in the Portuguese economy

This paper intends to analyse to what extent does a worker who, along with a job move undergoes a spatial move, gain a wage increase. For that matter, a sample of Quadros de Pessoal is used with information gathered regarding all the workers that are part of those tables, simultaneously for the years 1997 and 1998 as well as their working places. This information is initially used to carry out a bivariate analysis allowing characterizing the workers that change jobs, those who change working places and those who experience both changes. Afterwards, a wage equation is estimated, namely an Augmented Mincer Equation, taking into account both the hourly wage and the wage, making it possible to verify the influence of spatial mobility (through three levels of mobility, according to the distance between the old and new jobs) on the wage. In fact, the results of these estimations suggest that the longer the distance between the old and the new job, higher wage the moving worker will get. KEYWORDS Wage mobility, job mobility, spatial mobility, Portugal JEL Classification: J31, J61, J62, R23

On the constraints defining BPS monopoles

We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an important role in our analysis.Comment: 29 pages, 7 eps figure

Spontaneous CP Violation in the Next-to-Minimal Supersymmetric Standard Model Revisited

We re-examine spontaneous CP violation at the tree level in the context of the next-to-minimal supersymmetric standard model (NMSSM) with two Higgs doublets and a gauge singlet field. We analyse the most general Higgs potential without a discrete Z_3 symmetry, and derive an upper bound on the mass of the lightest neutral Higgs boson consistent with present experimental data. We investigate, in particular, its dependence on the admixture and CP-violating phase of the gauge singlet field, as well as on tan(beta). To assess the viability of the spontaneous CP violation scenario, we estimate epsilon_K by applying the mass insertion approximation. We find that a non-trivial flavour structure in the soft-breaking A terms is required to account for the observed CP violation in the neutral kaon sector. Furthermore, combining the minimisation conditions for spontaneous CP violation with the constraints coming from K0-K0bar mixing, we find that the upper bound on the lightest Higgs-boson mass becomes stronger. We also point out that the electric dipole moments of electron and neutron are a serious challenge for SUSY models with spontaneous CP violation.Comment: 19 pages, LaTeX2e, 5 figures; matches the published versio

A combinatorial formula for homogeneous moments

We establish a combinatorial formula for homogeneous moments and give some examples where it can be put to use. An application to the statistical mechanics of interacting gauged vortices is discussed.Comment: 8 pages, LaTe

Novel Supersymmetric SO(10) Seesaw Mechanism

We propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10) models with broken D-parity. It is shown that in such scenarios the B-L scale can be as low as TeV without generating inconsistencies with gauge coupling unification nor with the required magnitude of the light neutrino masses. This leads to a possibly light new neutral gauge boson as well as relatively light quasi-Dirac heavy leptons. These particles could be at the TeV scale and mediate lepton flavour and CP violating processes at appreciable levels.Comment: 4 pages, 3 figures, revtex4, references added, typos corrected, sharper discussion of the RGEs give

NATO: The Indispensable Western Alliance

A Research Paper Developed as part of the Air Command and Staff College program.The 21st century did not start well. Terrorism and war has marked every single year so far. It is not a good sign of what this century will be. In the last century, globalization, the victory over communism, a technology driven revolution, the chance of spreading a model of society thru the internet and modern communication systems, all allowed the rise of political awareness, envy and resentment against the West. The Western societies feel less secure now than they did during the Cold War period. Their values and beliefs are at stake. The problem is not only the asymmetric threats, it is also the political conflicts between Americans and Europeans. Instead of unifying efforts against a common threat, the Allies seem to be drifting further apart, and loosing the war. How can the West escape from this trap and guarantee the preservation of their values? This preservation is essential, so that future generations can have the opportunity to live in a free world and make their choices. NATO is the indispensable Alliance to the preservation of the western values. It is a tool capable of creating a bridge between American and European interests and identities and without it, the western stability will grow weaker. It is true the Allies are different to a certain extent. It is also true their cultural foundations are based on the same core democratic values and beliefs. Although because of their geography, history, nationalism/ethnicity, development and religion, they came to develop different external behaviors. Cultural differences are common and well accepted in both Europe and America. This is not the problem. The problem is diverging and conflicting external policies that separate the Allies and benefit terrorists. To prevent a strategic split it is indispensable to find and implement the right solution, aimed to preserve the Western Values and the freedom they represent. The first possible solution is the creation of ad hoc coalitions, every time a security problem appears. Operation Iraqi Freedom is a good example. Such solutions are not legitimate since they do not rely on international recognized and generally accepted institutions, such as the UNSC. It is not the way of defending the collective security the West needs, since Nations do not commit themselves to develop and enforce rules generally accepted by the international community. It does not guarantee the preservation of the western values, since it can create conflicts among the Allies, just as it happened during the Iraqi War, leaving them in a weaker political position. The second possibility is NATO being replaced by a completely separate European and American Militaries. A complete separation between western military institutions, more than serving the West would hurt the preservation of its values. A European Security and Defense Policy completely separated from NATO would mean that the forum of decision that NATO provides would no longer be available to filter interests and protect higher values. It would mean less unity to fight a common threat and address the global turmoil issues. The solution that matches the challenge is a NATO prepared and redefined for the 21st century and its challenges. It means the establishment of a new framework, within the North Atlantic Alliance. A new marriage of convenience is required, including what seems to be a multilateral Europe and a unilateral America. In the 21st century NATO, Europe needs to assume its full political and economic responsibilities. America needs to compromise its freedom of action towards effective institutionalism, in favor of a global leadership rather than global governance. Only strategically combining efforts can the West guarantee the preservation of freedom and other core democratic values

Quantum Chern-Simons Vortices on a Sphere

The quantisation of the reduced first-order dynamics of the nonrelativistic model for Chern-Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric quantisation on the moduli space of static solutions, using a Kaehler polarisation, to construct the quantum Hilbert space. Its dimension is related to the volume of the moduli space in the usual classical limit. The angular momenta associated with the rotational SO(3) symmetry of the model are determined for both the classical and the quantum systems. The results obtained are consistent with the interpretation of the solitons in the model as interacting bosonic particles