Quantum-induced interactions in the moduli space of degenerate BPS domain walls

In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a $(1+1)$-dimensional space-time the defects are classically degenerate in mass kinks, but in $(3+1)$ dimensions the kinks become BPS domain walls, all of them sharing the same surface tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum kink and domain wall fluctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to accommodate the infrared divergences due to zero modes in the spectra of the second-order kink and domain wall fluctuation operators, which are respectively $N\times N$ matrix ordinary or partial differential operators. Use of these tools in the spectral zeta function associated with the Hessian operators paves the way to obtain general formulas for the one-loop kink mass and domain wall tension shifts in any $(1+1)$- or $(3+1)$-dimensional $N$-component scalar field theory model. Application of these formulae to the BPS kinks or domain walls of the $N=2$ model mentioned above reveals the breaking of the classical mass or surface tension degeneracy at the quantum level. Because the main parameter distinguishing each member in the BPS kink or domain wall moduli space is essentially the distance between the centers of two basic kinks or walls, the breaking of the degeneracy amounts to the surge in quantum-induced forces between the two constituent topological defects. The differences in surface tension induced by one-loop fluctuations of BPS walls give rise mainly to attractive forces between the constituent walls except if the two basic walls are very far apart. Repulsive forces between two close walls only arise if the coupling is approaches the critical value from below.Comment: 34 pages, 7 figures, to appear in JHE

One-dimensional solitary waves in singular deformations of SO(2) invariant two-component scalar field theory models

In this paper we study the structure of the manifold of solitary waves in some deformations of SO(2) symmetric two-component scalar field theoretical models in two-dimensional Minkowski space. The deformation is chosen in order to make the analogous mechanical system Hamilton-Jacobi separable in polar coordinates and displays a singularity at the origin of the internal plane. The existence of the singularity confers interesting and intriguing properties to the solitary waves or kink solutions.Comment: 25 pages, 18 figure

On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts

In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schr\"odinger differential operators with P\"oschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and $\phi^4$ models.Comment: 23 pages, 4 figures, to be published in Annals of Physic

Higgs phase in a gauge U(1)\mathbf{U}(1) non-linear CP1\mathbf{CP}^1-model. Two species of BPS vortices and their zero modes

In this paper zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2\pi n$, $n\in \mathbb{Z}$, is the quantized magnetic flux of the two species of BPS vortex solutions, $2n$ linearly independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension $2n$ of these stringy topological defects is thus locally shown.Comment: 17 pages, 28 figure

Changing shapes: adiabatic dynamics of composite solitary waves

We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite non-linear non-dispersive waves points to variations in shape.Comment: 21 pages, 15 figures. To appear in Physica D: Nonlinear Phenomen

Two Species of Vortices in a massive Gauged Non-linear Sigma Model

Non-linear sigma models with scalar fields taking values on $\mathbb{C}\mathbb{P}^n$ complex manifolds are addressed. In the simplest $n=1$ case, where the target manifold is the $\mathbb{S}^2$ sphere, we describe the scalar fields by means of stereographic maps. In this case when the $\mathbb{U}(1)$ symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the self-dual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in $(2+1)$-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged $\mathbb{C}\mathbb{P}^2$ model in a Reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the $\mathbb{U}(1)\times\mathbb{S}\mathbb{U}(2)$ semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing $N$ complex scalar fields are easily generalized to gauged $\mathbb{C}\mathbb{P}^N$ models.Comment: 39 pages, 23 figures (extended version), to be published in JHE

Impact of the Timing of Metoprolol Administration During STEMI on Infarct Size and Ventricular Function.

BACKGROUND Pre-reperfusion administration of intravenous (IV) metoprolol reduces infarct size in ST-segment elevation myocardial infarction (STEMI). OBJECTIVES This study sought to determine how this cardioprotective effect is influenced by the timing of metoprolol therapy having either a long or short metoprolol bolus-to-reperfusion interval. METHODS We performed a post hoc analysis of the METOCARD-CNIC (effect of METOprolol of CARDioproteCtioN during an acute myocardial InfarCtion) trial, which randomized anterior STEMI patients to IV metoprolol or control before mechanical reperfusion. Treated patients were divided into short- and long-interval groups, split by the median time from 15 mg metoprolol bolus to reperfusion. We also performed a controlled validation study in 51 pigs subjected to 45 min ischemia/reperfusion. Pigs were allocated to IV metoprolol with a long ( 25 min) or short ( 5 min) pre-perfusion interval, IV metoprolol post-reperfusion (þ60 min), or IV vehicle. Cardiac magnetic resonance (CMR) was performed in the acute and chronic phases in both clinical and experimental settings. RESULTS For 218 patients (105 receiving IV metoprolol), the median time from 15 mg metoprolol bolus to reperfusion was 53 min. Compared with patients in the short-interval group, those with longer metoprolol exposure had smaller infarcts (22.9 g vs. 28.1 g; p ¼ 0.06) and higher left ventricular ejection fraction (LVEF) (48.3% vs. 43.9%; p ¼ 0.019) on day 5 CMR. These differences occurred despite total ischemic time being significantly longer in the long-interval group (214 min vs. 160 min; p < 0.001). There was no between-group difference in the time from symptom onset to metoprolol bolus. In the animal study, the long-interval group (IV metoprolol 25 min before reperfusion) had the smallest infarcts (day 7 CMR) and highest long-term LVEF (day 45 CMR). CONCLUSIONS In anterior STEMI patients undergoing primary angioplasty, the sooner IV metoprolol is administered in the course of infarction, the smaller the infarct and the higher the LVEF. These hypothesis-generating clinical data are supported by a dedicated experimental large animal study.post-print808 K

Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors

In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.Comment: 29 pages, 51 figure

The Kink variety in systems of two coupled scalar fields in two space-time dimensions

In this paper we describe the moduli space of kinks in a class of systems of two coupled real scalar fields in (1+1) Minkowskian space-time. The main feature of the class is the spontaneous breaking of a discrete symmetry of (real) Ginzburg-Landau type that guarantees the existence of kink topological defects.Comment: 12 pages, 5 figures. To appear in Phys. Rev.

New models for two real scalar fields and their kinklike solutions

In this work we study the presence of kinks in models described by two real scalar fields in bi-dimensional space-time. We generate new two-field models, constructed from distinct but important one-field models, and we solve them with techniques that we introduce in the current work. We illustrate the results with several examples of current interest to high energy physics.Comment: 8 pages, 6 figures; To appear in Adv. High Energy Phy