arXiv subjects

Juan Mateos-Guilarte

Publications and source records attributed to Juan Mateos-Guilarte.

4 recordsLinked to original sources

arXiv2016

Higgs phase in a gauge $\mathbf{U}(1)$ non-linear $\mathbf{CP}^1$-model. Two species of BPS vortices and their zero modes

In this paper zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2πn$, $n\in \mathbb{Z}$, is the quantized magnetic flux of the two species of BPS vortex solutions, $2n$ linearly independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension $2n$ of these stringy topological defects is thus locally shown.

hep-th↗

arXiv2013

Gilkey-de Witt heat kernel expansion and zero modes

In this paper we propose a generalization of the Gilkey-de Witt heat kernel expansion, designed to provide us with a precise estimation of the heat trace of non-negative Schroedinger type differential operators with non-trivial kernel over all the domain of its "inverse temperature" variable. We apply this modified approach to compute effectively the one-loop kink mass shift for some models whose kink fluctuation operator spectrum is unknown and the only alternative to estimate this magnitude is the use of the heat kernel expansion techniques.

hep-th↗

arXiv2012

Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat kernel expansion.

hep-th↗

arXiv2012

On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts

In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $ϕ^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schrödinger differential operators with Pöschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and $ϕ^4$ models.

hep-th↗