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W. Garcia Fuertes

Publications and source records attributed to W. Garcia Fuertes.

At least 19 recordsLinked to original sources
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↗
arXiv2015

A note on BPS vortex bound states

In this note we investigate bound states, where scalar and vector bosons are trapped by BPS vortices in the Abelian Higgs model with a critical ratio of the couplings. A class of internal modes of fluctuation around cylindrically symmetric BPS vortices is characterized mathematically, analysing the spectrum of the second-order fluctuation operator when the Higgs and vector boson masses are equal. A few of these bound states with low values of quantized magnetic flux are described fully, and their main properties are discussed.

hep-th↗
arXiv2009

Quantum fluctuations around low-dimensional topological defects

In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it is first applied to various types of kinks arising in several deformed linear and non-linear sigma models with different numbers of scalar fields. In the second part, the same conceptual framework is constructed for the topological solitons of the planar semilocal Abelian Higgs model, built from a doublet of complex scalar fields and one U(1) gauge field.

hep-th↗
arXiv2008

One-loop fluctuations of semi-local self-dual vortices

Mass shifts induced by one-loop fluctuations of semi-local self-dual vortices are computed. The procedure is based on canonical quantization and heat kernel/ zeta function regularization methods. The issue of the survival of the classical degeneracy in the semi-classical regime is explored.

hep-th↗
arXiv2007

One loop corrections to the mass of self-dual semi-local planar topological solitons

A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU(2), and local (gauge), U(1), symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is of 90 degrees. The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.

hep-th↗
arXiv2007

Lectures on the mass of topological solitons

In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum fluctuations is the trace of the square root of the differential operator governing these fluctuations. Standard mathematical techniques are used to deal with some powers of pseudo-differential operators. Ultraviolet divergences are tamed by using generalized zeta function regularization methods and, then performing zero-point energy and mass renormalizations.

hep-th↗
arXiv2005

Quantum trigonometric Calogero-Sutherland model, irreducible characters and Clebsch-Gordan series for the exceptional algebra E7

We re-express the quantum Calogero-Sutherland model for the Lie algebra E7 and the particular value of the coupling constant K=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra.

math-ph↗
arXiv2005

Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices

The mass shift induced by one-loop quantum fluctuations on self-dual ANO vortices is computed using heat kernel/generalized zeta function regularization methods. The quantum masses of super-imposed multi-vortices with vorticity lower than five are given. The case of two separate vortices with a quantum of magnetic flux is also discussed.

hep-th↗
arXiv2004

One-loop correction to classical masses of quantum kink families

One-loop corrections to kink masses in a family of (1+1)-dimensional field theoretical models with two real scalar fields are computed. A generalized DHN formula applicable to potentials with and without reflection is obtained. It is shown how half-bound states arising in the spectrum of the second order fluctuation operator for one-component topological kinks and the vacuum play a central r$\hat{\rm o}$le in the computation of the kink Casimir energy. The issue of whether or not the kink degeneracy exhibited by this family of models at the classical level survives one-loop quantum fluctuations is addressed.

hep-th↗
arXiv2003

Degenerate BPS Domain Walls: Classical and Quantum Dynamics

We discuss classical and quantum aspects of the dynamics of a family of domain walls arising in a generalized Wess-Zumino model. These domain walls can be embedded in ${\cal N}=1$ supergravity as exact solutions and are composed of two basic lumps.

hep-th↗
arXiv2002

Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two ${\rm P}(ϕ)_2$ systems with polynomial self-interactions.

hep-th↗