Exact Renormalization of Massless QED2

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.Comment: 14 pages, no figures, introduction and conclusions modifie

In-Situ Component-Based TPA for Time-Variant Dynamic Systems: A State-Space Formulation

In this chapter, a methodology to calculate equivalent forces by taking into account the possible time-varying dynamic behavior of the components under analysis is presented. This methodology is based on the use of the state-space realization of the in-situ component-based TPA method. To take into account possible time-varying dynamic behavior of the systems under study, a local linear parameter varying (LPV) model identification approach is used. This approach enables the computation of state-space models representative of the components at each time instant by interpolating a given set of linear time-invariant (LTI) state-space models representative of the dynamics of the components under study for fixed operating conditions. By exploiting a numerical example, it is found that when dealing with structures presenting time-varying behavior, accurate equivalent forces can be computed in time domain by using the approaches presented in this chapter. Furthermore, it is clearly demonstrated that ignoring the time dependency of the dynamic behavior of mechanical systems can lead to an important deterioration of the results

Melvin solution with a dilaton potential

We find new Melvin-like solutions in Einstein-Maxwell-dilaton gravity with a Liouville-type dilaton potential. The properties of the corresponding solution in Freedman-Schwarz gauged supergravity model are extensively studied. We show that this configuration is regular and geodesically complete but do not preserve any supersymmetry. An exact solution describing travelling waves in this Melvin-type background is also presented.Comment: 12 pages, LaTeX, no figure

An experience with Desmos in the study of the quadratic function

In this paper we present a didactic experience in the subject of Mathematics carried out in a distance learning context, on the topic Quadratic Function, using the digital and free platform Desmos. The use of this tool was determinant for the teaching and learning of quadratic function since its teaching took place in distance education, due to the pandemic situation. In a pandemic context, the use of tools to gauge student learning was a necessity, but practices such as the one described in this paper should be incorporated into a normal classroom environment, promoting discovery through graphical and algebraic manipulation.publishe

Gregory-Laflamme instability of a slowly rotating black string

We study the Gregory-Laflamme instability of a 5-dimensional slowly rotating black string in which the 4-dimensional section is described by the Kerr black hole. We treat the rotation in a perturbative way introducing a small parameter for the rotation. It is found that rotation makes the Gregory-Laflamme instability stronger. Both the critical wavelength at the onset of instability and the growth time-scale are found to decrease as the rotation increases.Comment: 26 pages, 1 figur

On the Renormalizability of Theories with Gauge Anomalies

We consider the detailed renormalization of two (1+1)-dimensional gauge theories which are quantized without preserving gauge invariance: the chiral and the "anomalous" Schwinger models. By regularizing the non-perturbative divergences that appear in fermionic Green's functions of both models, we show that the "tree level" photon propagator is ill-defined, thus forcing one to use the complete photon propagator in the loop expansion of these functions. We perform the renormalization of these divergences in both models to one loop level, defining it in a consistent and semi-perturbative sense that we propose in this paper.Comment: Final version, new title and abstract, introduction and conclusion rewritten, detailed semiperturbative discussion included, references added; to appear in International Journal of Modern Physics

A note on Kerr/CFT and free fields

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL(2,R) x U(1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.Comment: 10 pages, v2: comments and references adde