arXiv subjects

U. Camara da Silva

Publications and source records attributed to U. Camara da Silva.

6 recordsLinked to original sources

arXiv2025

Universal BPS Structure of Scalar Kinks in Static Geometries

We present a geometric extension of the Bogomolny-Prasad-Sommerfield (BPS) construction for scalar kinks in (1+1) dimensions embedded in static curved spacetimes. By introducing a nonminimal coupling between the scalar prepotential and the extrinsic curvature of the static foliation, the flat-space first-order Bogomolny equation remains exactly valid for arbitrary static backgrounds. As a consequence, the kink profile is unchanged, while the effective potential and vacuum structure acquire a controlled geometric dependence. We show that these curved-space BPS kinks are always linearly stable. However, the existence of the translational zero mode is not guaranteed: its normalizability depends on the competition between the intrinsic length scale of the kink and the asymptotic curvature scale of the geometry. When the geometric scale dominates, the zero mode is removed and the soliton becomes geometrically pinned, despite remaining an exact BPS solution. Explicit realizations in AdS2 demonstrate how different static slicings of the same spacetime lead to qualitatively distinct physical outcomes, ranging from preserved translational invariance to its complete removal by horizons. These results establish geometry as a precise mechanism for controlling solitonic moduli without compromising linear stability.

hep-th↗

arXiv2025

Renormalization of Schrödinger equation for potentials with inverse-square singularities: Generalized Trigonometric Pöschl-Teller model

We introduce a renormalization procedure necessary for the complete description of the energy spectra of a one-dimensional stationary Schrödinger equation with a potential that exhibits inverse-square singularities. We apply and extend the methods introduced in our recent paper on the hyperbolic Pöschl-Teller potential (with a single singularity) to its trigonometric version. This potential, defined between two singularities, is analyzed across the entire bidimensional coupling space. The fact that the trigonometric Pöschl-Teller potential is supersymmetric and shape-invariant simplifies the analysis and eliminates the need for self-adjoint extensions in certain coupling regions. However, if at least one coupling is strongly attractive, the renormalization is essential to construct a discrete energy spectrum family of one or two parameters. We also investigate the features of a singular symmetric double well obtained by extending the range of the trigonometric Pöschl-Teller potential. It has a non-degenerate energy spectrum and eigenstates with well-defined parity.

quant-ph↗

arXiv2020

Conformal Scale Factor Inversion for Domain Walls and Holography

We describe a correspondence between domain wall solutions of Einstein gravity with a single scalar field and self-interaction potential. The correspondence we call 'conformal scale factor inversion (CSFI)' is a map comprising the inversion of the scale factor in conformal coordinates, and a transformation of the field and its potential which preserves the form of the Einstein equations for static and isotropic domain walls. By construction, CSFI maps the asymptotic AdS boundary to the vicinity of a naked singularity in a theory with a special Liouville (exponential) scalar field potential; it is also a map in the parameter space of exponential potentials. The correspondence can be extended to linear fluctuations, being akin to an S-duality, and can be interpreted in terms of 'SUSY quantum mechanics' for the fluctuation modes. The holographic implementation of CSFI relates the UV and IR regimes of a pair of holographic renormalization group flows; in particular, it is a symmetry of the GPPZ flow.

hep-th↗

arXiv2019

SUSY shields the scaling symmetry of conformal quantum mechanics

Renormalization of the inverse square potential usually breaks its classical conformal invariance. In a strongly attractive potential, the scaling symmetry is broken to a discrete subgroup while, in a strongly repulsive potential, it is preserved at quantum level. In the intermediate, weak-medium range of the coupling, an anomalous length scale appears due to a flow of the renormalization group away from a critical point. We show that potentials with couplings in the strongly-repulsive and in the weak-medium ranges can be related by a dynamical supersymmetry. Imposing SUSY invariance unifies these two ranges, and fixes the anomalous scale to zero, thus restoring the continuous scaling symmetry.

hep-th↗

arXiv2018

Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude

The Aharonov-Bohm elastic scattering with incident particles described by plane waves is revisited by using the phase-shifts method. The formal equivalence between the cylindrical Schrödinger equation and the one-dimensional Calogero problem allows us to show that up to two scattering phase-shifts modes in the cylindrical waves expansion must be renormalized. The renormalization procedure introduces new length scales giving rise to spontaneous breaking of the conformal symmetry. The new renormalized cross-section has an amazing property of being non-vanishing even for a quantized magnetic flux, coinciding with the case of Dirac delta function potential. The knowledge of the exact beta function permits us to describe the renormalization group flows within the two-parametric family of renormalized Aharonov-Bohm scattering amplitudes. Our analysis demonstrates that for quantized magnetic fluxes a BKT-like phase transition at the coupling space occurs.

hep-th↗

arXiv2016

On the thermodynamics of scale factor dual Universes

The thermodynamical aspects of the conformal time scale factor duality (SFD) of cosmological models within Einstein Gravity are investigated. We derive the SFD transformations of the thermodynamical quantities describing the thermal evolution of the matter fluid and of the apparent horizon. The thermodynamical properties of the self-dual cosmological models with a modified Chaplygin gas are studied in detail. We deduce the restrictions on the equation of state parameters that allow to extend scale factor duality as a UV/IR symmetry of the cosmological models consistent with their thermodynamical behavior.

hep-th↗