arXiv subjects

G. S. Santiago

Publications and source records attributed to G. S. Santiago.

6 recordsLinked to original sources

arXiv2026

Scalar fields, impurities and supersymmetry

We develop a rigid $\mathcal{N}=(1,1)$ superspace formulation for multifield scalar models coupled to localized impurities through spurion superfields in two-dimensional spacetime. The spurionic completion gives a manifestly supersymmetric action and provides a systematic framework for describing interacting scalar fields in the presence of impurity backgrounds. In this setting, supersymmetry acts as an organizing principle for a controlled bosonic half-BPS sector, with the preserved projector selecting the impurity-compatible first-order equations. We derive the corresponding coupled BPS equations, energy density, boundary conditions, and Bogomol'nyi bound, showing that localized impurities deform the BPS profiles and redistribute the local energy density while leaving the total BPS energy fixed by the topological boundary term. We illustrate the formalism through representative one-, two-, and three-field models, analyzing the resulting BPS configurations and their local energy density profiles.

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arXiv2026

Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints

We investigate a class of models described by two real scalar fields in two-dimensional spacetime. The study focuses mainly on the presence of exact static solutions which satisfy the first-order formalism, in models constructed to engender Lorentz symmetry violation. We start by exploring a direct connection between Lorentz breaking and geometric constraint, as experimentally examined in the case of domain walls in geometrically constrained magnetic materials. By means of a specific choice of functions, we show that imposing geometric constraint within the Lorentz-violating framework recovers the exact solutions of the corresponding Lorentz-invariant theory. Furthermore, we extend the investigation to new models that go beyond reproducing the Lorentz invariant geometrically constrained solutions, revealing that it remains possible to parametrize the first-order equation of one of the fields through a suitably redefined coordinate.

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arXiv2025

Exact solutions for a complex scalar field under discrete symmetry

We report on the presence of families of exact solutions for a complex scalar field that behaves according to the rules of discrete $Z_N$ symmetry. Since the family of models is exactly solved, the results appear to be of interest to integrability, to build junctions and networks of localized structures and to describe scalar dark matter in high energy physics.

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arXiv2024

Localized structures in three-field models: geometrically constrained configurations and the first-order framework

This work deals with models described by three real scalar fields in one spatial dimension. We study the case where two of the three fields engender kinematical modifications, which respond as geometrical constrictions, that can be used to change the center and/or the tails of the kinklike configurations. An important advantage of our procedure is the construction of a method for the obtention of first-order differential equations that solve the equations of motion and give rise to stable localized structures. We illustrate the general procedure investigating several distinct examples, and suggesting some possibilities of applications of practical use, in particular, to the case of domain walls and skyrmions in magnetic material, collisions of kinks and to deal with braneworld scenarios having a warped five-dimensional anti de Sitter geometry, with a single extra dimension of infinite extent.

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arXiv2024

Kink Crystal

We describe a one-dimensional kink crystal, which represents a collection of equal and equally localized kinks forming a lattice in the real axis. The results are analytical, original and may motivate other studies on localized structures in high energy physics.

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arXiv2024

Geometrically Constrained Localized Configurations: First-Order Framework and Analytical Solutions

This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the kinetic term of one of the two fields. We elaborate on the construction of a first-order framework, which directly contributes to find analytical solutions. We describe several distinct possibilities, in particular, the case where the first-order equations do not separate. This is much harder, but we use the integrating factor to deal with analytical configurations. The proposed methodology help us deal with localized structures of both the Néel and Bloch type very naturally, and we end the work suggesting some possibilities of applications in distinct areas of nonlinear science.

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