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A. Alonso-Izquierdo

Publications and source records attributed to A. Alonso-Izquierdo.

At least 19 recordsLinked to original sources
arXiv2026

Scattering of wobbling vortices

We investigate the dynamical role of internal vibrational modes in the Abelian Higgs model, focusing on how Derrick-type excitations modify vortex dynamics and scattering processes. We study the scattering of excited vortices and show that the interplay between spectral flow and mode excitation generates effective forces and enables resonant energy transfer between translational and internal degrees of freedom. As a result, vortex dynamics become strongly non-adiabatic, exhibiting super-elastic collisions, oscillatory dependence of the final state on initial conditions, and the emergence of fractal structures in scattering diagrams. Our results demonstrate that internal vibrational modes play a fundamental role in vortex interactions, going beyond the standard moduli space approximation and revealing a rich phenomenology driven by mode dynamics.

hep-th↗
arXiv2026

BPS and semi-BPS kink families in two-component scalar field theories with fourth-degree polynomial potentials

We perform a systematic study of kink solutions in two-component scalar field theories in $(1+1)$ dimensions with interaction terms of at most quartic order. Our approach is based on the Bogomolny formalism, constructing scalar potentials from suitable superpotentials and analyzing the corresponding first-order equations. While cubic polynomial superpotentials naturally generate quartic interactions, we show that more general functional forms also lead to admissible models within the same class. In this way, we identify new models supporting continuous families of kinks with nontrivial internal structure, such that they can be interpreted as composite configurations formed by multiple localized energy lumps.

hep-th↗
arXiv2025

Kinks in composite scalar field theories

In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models, but also provides a framework for constructing more general families of field theories that inherit certain analytical information about their solutions. Specifically, this method combines two known field theories into a new composite field theory whose target space is the product of the original target spaces. By suitably coupling the fields through a superpotential defined on the product space, the dynamics in the subspaces become entangled while preserving original kinks as boundary kinks. Different composite field theories are studied, including extensions of well-known models to wider target spaces.

hep-th↗
arXiv2025

Spectral structure of fluctuations around $n$-vortices in the Abelian-Higgs model

We study in detail the internal structure of rotationally invariant higher-charge Abelian-Higgs vortices. The symmetry of the normal modes close to the critical regime for type II vortices determines the possible disintegration channels. The full internal mode structure is discussed, finding modes that conserve the vortex symmetry (Derrick type modes) and modes whose symmetry differs (multipolar modes).

hep-th↗
arXiv2025

Excited oscillons and charge-swapping

We show that the charge-swapping phenomenon can be understood as a real valued oscillon carrying an excitation in imaginary direction in the target space. Furthermore, we introduce a two dimensional collective model which quantitatively captures the charge swapping dynamics.

hep-th↗
arXiv2025

Dynamics of Excited BPS 3-Vortices

We analyze the dynamics of BPS 3-vortex solutions. First, for unexcited vortices, we study the 2-dimensional moduli space of centred vortices with $y \to -y$ symmetry, and its metric. We identify the 1-dimensional subspaces describing the head-on collisions of equidistant collinear and equilateral triangle configurations, where geodesic motion results in $90^\circ$ and 60^\circ$ scattering, respectively. Second, by studying the frequency spectrum of vibrational shape modes along these subspaces, we explain how the force-free, geodesic motion is modified by shape mode excitations into a pattern of chaotic multi-bounce collisions.

hep-th↗
arXiv2024

Transference of kinks between $\mathbb{S}^2$ and $\mathbb{R}^2$ Sigma models

In this paper methods for deforming scalar field theories on Euclidean target spaces, in which new field theories are constructed so that solutions are known, are generalized to the context of Sigma models. In particular, deformations between Sigma models on the plane and on the sphere are considered. Three different examples are presented, where the change in the structure of the kink variety and the energy of the deformed kinks during this procedure are studied.

hep-th↗
arXiv2024

Stability and decay of composite kinks/$Q$-balls solutions in a deformed $O(2N+1)$ linear sigma model

The defect-type solutions of a deformed $O(2N+1)$ linear sigma model with a real and $N$ complex fields in $(1+1)$-dimensional Minkowski spacetime are studied. All the solutions are analytically found for the $N=2$ case. Two types of solitons have been determined: (a) Simple solutions formed by a topological kink with or without the presence of a $Q$-ball. (b) Composite solutions. They are constituted by some one-parameter families of solutions which can be understood as a non-linear combination of simple solutions. The properties of all of those solutions and the analysis of their linear stability, as well as decay channels, are discussed.

hep-th↗
arXiv2024

Scattering between orthogonally wobbling kinks

The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions have two shape modes (one longitudinal and one orthogonal to the kink orbit), in addition to the zero mode, and in which energy redistribution can occur among these three discrete modes. We investigate the scattering between wobbling kinks whose orthogonal shape mode is initially excited, examining how the final velocities, amplitudes, and frequencies depend on the initial excitation amplitude. The differences that this model presents with respect to the $ϕ^4$ model and its novel properties are highlighted. This analysis sheds light on the intricate dynamics that arise from the interplay between multiple degrees of freedom in kink scattering processes, offering insights distinct from those observed in simpler models.

hep-th↗
arXiv2024

Collective Coordinate Models for 2-Vortex Shape Mode Dynamics

Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space $M$, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on $M$, modified by a potential, when the mode oscillations are fast relative to the moduli space motion and their amplitudes are small. When the lowest-frequency mode is excited with a large amplitude, the geodesic flow is not a correct description. Instead, a chaotic, or even fractal, multi-bounce structure in vortex-vortex collisions is predicted.

hep-th↗
arXiv2024

Excited Abelian-Higgs vortices: decay rate and radiation emission

The evolution of 1-vortices when their massive bound mode is excited is investigated in detail (both analytically and numerically) in the Abelian-Higgs model for different ranges of the self-coupling constant. The dependence of the spectrum of the 1-vortex fluctuation operator on the model parameter is discussed initially. A perturbative approach is employed to study the radiation emission in both the scalar and the vector channels. Our findings reveal that the oscillating initial configuration of the 1-vortex radiates at a frequency twice that of the internal mode. Through energy conservation considerations, we derive the decay law of the massive mode. Finally, these analytical results are compared with numerical simulations in field theory.

hep-th↗
arXiv2023

Geometric Construction of non-linear Sigma models with Q-ball/Q-kink solutions

Non-linear Sigma models involving U(1) symmetry group are studied using a geometrical formalism. In this type of models, Q-balls and Q-Kinks solutions are found. The geometrical framework described in this article allows the identification of the necessary conditions on the metric and the potential to guarantee the existence of these Q-balls and Q-Kinks. Using this procedure, Sigma models where both types of solutions coexist, have been identified. Only the internal rotational frequency distinguishes which one of these defects will arise.

hep-th↗
arXiv2023

Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space

The flow of shape eigenmodes of the small fluctuation operator around BPS 2-vortex solutions is calculated, as a function of the intervortex separation $2d$. For the rotationally-invariant 2-vortex, with $d = 0$, there are three discrete modes; the lowest is non-degenerate and the upper two are degenerate. As $d$ increases, the degeneracy splits, with one eigenvalue increasing and entering the continuous spectrum, and the other decreasing and asymptotically coalescing with the lowest eigenvalue, where they jointly become the eigenvalue of the 1-vortex radial shape mode. The behaviour of the eigenvalues near $d=0$ is clarified using a perturbative analysis, and also in light of the 2-vortex moduli space geometry.

hep-th↗
arXiv2023

Wobbling kinks and shape mode interactions in a coupled two-component $ϕ^4$ theory

The dynamics of a wobbling kink in a two-component coupled $ϕ^4$ scalar field theory (with an excited orthogonal shape mode) is addressed. For this purpose, the vibration spectrum of the second order small kink fluctuation is studied in order to find the corresponding vibration modes associated to the first (longitudinal) and second (orthogonal) field components. By means of this analysis, it was found that the number of possible shape modes depends on the value of the coupling constant. It is notable that when one of the orthogonal field shape modes is initially triggered, the unique shape mode of the longitudinal field is also activated. This coupling causes the kink to emit radiation with twice the frequency of excited mode in the first field component. Meanwhile, in the orthogonal channel we find radiation with two different frequencies: one is three times the frequency of the orthogonal wobbling mode and another is the sum of the frequencies of the longitudinal shape mode and the triggered mode. All the analytical results obtained in this study have been successfully contrasted with those obtained through numerical simulations.

nlin.PS↗
arXiv2023

Semi-BPS sphaleron and its dynamics

We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity. This means that there is no static force between the sphaleron and the impurity. Therefore such a sphaleron-impurity system is very much like usual BPS multi-solitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system.

hep-th↗
arXiv2023

Topological and non-topological kink families in non-linear $(\mathbb{S}^1\times \mathbb{S}^1)$-Sigma models

In this paper we construct a family of Hamilton-Jacobi separable non-linear $\mathbb{S}^1\times\mathbb{S}^1$ Sigma models for which the kink variety can be analytically identified and for which the linear stability of the emerging kinks is ensured. Furthermore, a model with only one vacuum point is found, where all kinks are forced to be non-topological. The non-simply connectedness of the torus guarantees the global stability of all the non-topological kinks in these models.

hep-th↗