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M. A. Liao

Publications and source records attributed to M. A. Liao.

14 recordsLinked to original sources
arXiv2026

Topological solitons of two-field scalar theories in rotationally symmetric backgrounds

This work concerns scalar field theories with topologically nontrivial vacuum manifold in rotationally symmetric backgrounds of arbitrary dimension. Lagrangians with canonical and generalized kinetic terms are considered, and a Bogomol'nyi framework is developed for the symmetric restriction of the theory. Localized topological solutions are found. Their stability, which would normally be prevented in higher dimensions due to scaling instability, is made possible by the presence of an explicit radial dependence on the potential. The first-order equations give rise to an integrable orbit equation which can be used to solve the problem completely. It is shown that target space orbits - but not the solutions themselves - are shared between analogous systems defined in different backgrounds. Moreover, the first-order equations can be mapped into a one-dimensional BPS theory through a transformation encoded by a function $ξ(r)$. The internal structure, size and existence of defects follows from the properties and range of this mapping. We use these tools to evaluate the effect of geometry on confinement, existence, and structure of solitons. Exact solutions are provided in Minkowski, Schwarzschild, de Sitter, Schwarzschild de Sitter and conformally flat backgrounds.

hep-th↗
arXiv2026

Geometrically constrained multi-kink configurations in generalized impurity-doped field theories

This short communication investigates impurity coupling in generalized field theories where scalar coupling is introduced directly at the level of the kinetic and gradient contributions of the energy. We show that the fundamental aspects of the original theory, which has been previously investigated in the impurity-free setting, can be extended to the inhomogeneous scenario. In particular, an interpretation in terms of geometrically-constrained effective one-field theories with impurities is possible in the separable case. We show that BPS multi-kink configurations are possible in the model, as well as in the usual half-BPS scalar theories.

hep-th↗
arXiv2026

Tidal perturbations and Love Symmetry for five-dimensional charged rotating black holes

We investigate the tidal response of general five-dimensional (5D) black holes of STU supergravity, which include as special cases important solutions such as the Myers-Perry, BMPV, 5D Reissner-Nordström, Kerr-Newman and dyonic black holes. Solutions are parameterized by their mass, two angular momenta and up to three $U(1)$ charges. Love numbers and dissipation coefficients are obtained in the static and dynamic cases. In the latter scenario, we find new, nontrivial conditions, realized in important limiting cases of the theory, such as the BPS limit, where frequency-independent vanishing conditions are obtained. We also develop a ladder formalism for static solutions and derive the conserved charges. To the best of our knowledge, this formalism had not been previously derived for 5D black holes, including neutral ones. Finally, we show the emergence of Love symmetry in the near-zone regime, and derive the generators of the associated $sl(2,\mathbb{R})$ algebra. It is shown that all conditions for Love-number vanishing can be explained by this algebra in terms of the highest-weight property.

hep-th↗
arXiv2025

Magnetic monopoles in Yang-Mills-Higgs theory with impurities

In this work, BPS models built from the coupling of Yang-Mills-Higgs Lagrangian to impurities are investigated. We first consider scalar impurities, which in the BPS limit generate monopoles similar to those obtained in a previously considered class of $\mathrm{SU(2)}\times\mathrm{Z}_2$ or $\mathrm{SU(2)}\times\mathrm{SU(2)}$ models. We then focus on coupling with nonabelian impurities, defined as fixed backgrounds produced from fields transforming under the adjoint representation of SU(2), with a coupling chosen to preserve half of the BPS sectors. The nature of this coupling, the ensuing Bogomol'nyi bound and BPS equations, as well as the effect of these impurities in the abelianization that leads to the emergence of a U(1) gauge group are investigated. We study in greater detail impurities with spherical symmetry, and examine the manner in which impurity coupling changes the asymptotic behavior and range of monopole interactions. Moreover, we introduce a method that can be used to approximate solutions with the use of small perturbations around the Prasad-Sommerfield monopole, and discuss the possibility of extending the aforementioned results to dyons. In order to exemplify the most important properties of the theory, several specific impurity models are presented, with the respective monopole solutions are found numerically. These solutions present novel internal structure and multiple features that would not be possible in the original theory.

hep-th↗
arXiv2024

Two-field models in the presence of impurities

This work deals with systems of two real scalar fields coupled to impurity functions, meant to model inhomogeneities often encountered in real physical applications. We investigate the theoretical properties of these systems and some of the consequences of impurity doping. We show that the theory may be modified in a way that preserves some BPS sectors, while also greatly impacting the behavior and internal structure of the solution, and exemplify those results with an investigation of a few interesting models in which impurities are coupled to a theory with a quartic potential. It is shown that, in the presence of impurities, the asymptotic behavior of field configurations may be changed, leading to solutions with different long-range properties, which are relevant to several physical applications. Our examples also highlight other important consequences that may follow from the addition of impurities, such as the presence of zero-modes that can significantly change the internal structure of a given solution without altering its energy, the creation of new topological sectors that did not exist in the impurity-free theory, and the possibility of stable, nontrivial configurations generated by topologically trivial boundary conditions. We have also shown that it is sometimes possible to find energy minimizers in BPS sectors which were unpopulated in the canonical theory. These features show that impurities allow for significant flexibility in both the form of energy minimizers and the boundary conditions used to generate them, which may potentially broaden the range of applicability of the theory.

hep-th↗
arXiv2024

Impurity-doped stable domain walls in spherically symmetric spacetimes

In this work, radially symmetric kink-like solutions in the presence of impurities are investigated for both flat and curved $D+1$ spacetimes, with geometry generated by a rotationally invariant background metric. We have examined the constraints placed upon the model by Derrick's theorem, and found out the Bogomol'nyi bound and equations of the symmetric restriction to this theory. Impurity-doped versions of a $ϕ^4$ model in two dimensions and a model with logarithmic potential in a Schwarzschild background have been explicitly worked out. The resulting configurations have been compared with those found in the homogeneous version of the theory, so that the effect of impurities in the form of solutions may be better appreciated. We have also generalized to higher dimensions some of the results that had been presented in the recent literature. These results relate to the possibility of BPS-preserving impurities, which we have found to still exist in the spacetimes considered in this work. We also investigate ways in which these results may be extended in a curved background.

gr-qc↗
arXiv2023

Higher Spin Mode Stability for STU Black Hole Backgrounds

This work studies mode stability of an STU black hole with four pairwise equal $\rm{U(1)}$ charges in four spacetime dimensions. We investigate bosonic perturbations for probe fields of different spins through the transformation technique devised by Whiting in 1989. Finally, we introduce connection relations inspired by the work of ~Duztaş (2016) to prove the absence of unstable modes that solve the torsion-modified Dirac equation appropriate for this black hole background.

gr-qc↗
arXiv2023

Impurity-doped scalar fields in arbitrary dimensions

We investigate the presence of localized structures for relativistic scalar fields coupled to impurities in arbitrary spatial dimensions. Such systems present spatial inhomogeneity, realized through the inclusion of explicit coordinate dependence in the Lagrangian. It is shown that, in stark contrast to the impurity-free scenario, Derrick's argument does not present a strong hindrance to the existence of stable solutions in this case. Bogomol'nyi equations giving rise to global minima of the energy are found, and some of the ensuing BPS configurations are presented.

hep-th↗
arXiv2022

Generalized Maxwell-Higgs vortices in models with enhanced symmetry

Topological vortices in relativistic gauge theories in flat three-dimensional spacetime are investigated. We consider the symmetry $\rm{U(1)}\times...\times \rm{U(1)}$, and for each $\rm{U(1)}$ subgroup, a complex scalar field transforming under its action is introduced, as well as generalized permeabilities through which the subsystems are coupled. We investigate in detail the features of static, finite energy solutions within this class of generalized Maxwell-Higgs models, and study the effect of the winding numbers in the magnetic properties of each subsystem. A BPS bound and the related first order equations are introduced for a large class of models. Finally, we present some specific models and solve their equations of motion to find solutions engendering many distinct features in relation to each other and to the standard Nielsen-Olesen vortex.

hep-th↗
arXiv2021

Impurity-like solutions in vortex systems coupled to a neutral field

In this work, a Maxwell-Higgs system is coupled to a neutral scalar field that engenders $Z_2$ symmetry. At critical coupling, the resulting field equations may be identified with those of a Maxwell-Higgs model doped with an impurity whose form changes according to properties of the neutral scalar field, such as the topological sector and position of its zeros. This allows for an interpretation of parameters appearing in impurity models in terms of properties of the kink-like defect, and provides a convenient way to understand and generate impurities. By solving the first order equations, we found vortices with a novel internal structure in relation to standard solutions. The procedure was also adapted to generate impurities for Chern-Simons-Higgs theory.

hep-th↗
arXiv2021

Multimagnetic Monopoles

In this work we investigate the presence of magnetic monopoles that engender multimagnetic structures, which arise from an appropriate extension of the $\rm{SU(2)}$ gauge group. The investigation is based on a modified relativistic theory that contain several gauge and matter fields, leading to a Bogomol'nyi bound and thus to a first order framework, from which stable multimagnetic solutions can be constructed. We illustrate our findings with several examples of stable magnetic monopoles with multimagnetic properties.

hep-th↗
arXiv2020

Geometrically Constrained Kinklike Configurations

In this work we study kinklike structures, which are localized solutions that appear in models described by real scalar fields. The model to be considered is characterized by two real scalar fields and includes a function of one of the two fields that modifies the kinematics associated to the other field. The investigation brings to light a first order framework that minimizes the energy of the solutions by introducing an auxiliary function that directly contributes to describe the system. We explore an interesting route, in which one field acts independently, entrapping the other field, inducing important modifications in the profile of the localized structure. The procedure may make the solution to spring up as a kinklike configuration with internal structure, engendering the important feature that also appears directly connected with issues of current interest at the nanometric scale, in particular in the electronic transport in molecules in the presence of vibrational degrees of freedom.

hep-th↗
arXiv2019

Multilayered Vortices

Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender integer winding number and appear under the presence of a local Abelian symmetry. In this work we study vortices in a Maxwell-Higgs model, in which the gauge symmetry is enhanced to accommodate additional symmetries, responsible to generate localized structures to be used to constrain the vortex structure in a given region in the plane. The main aim is to examine how the vortex profile changes when it inhabits a limited region, an issue of current interest to the study of vortices at the nanometric scale.

hep-th↗