3.10 Tesis magíster

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Browsing 3.10 Tesis magíster by Author "Bañados, Máximo"

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    Espacio overspinning y singularidades en espacios BTZ
    (2023) Briceño Catalán, Matías Sebastián Camilo; Bañados, Máximo; Martínez, Cristián; Pontificia Universidad Católica de Chile. Instituto de Física
    En esta tesis se estudia el espacio Overspinning, solución a las ecuaciones de Einstein con constante cosmológica negativa (-1/ L^2) en 2+1 dimensiones tal que su momentum angular J sea mayor en módulo a su masa M, esto es, |J |> L |M| . Este espacio-tiempo comparte métrica con el agujero negro BTZ, pero al estar en otro rango de valores de (M,J) no posee horizonte de eventos, dando lugar a una singularidad desnuda. Se encontra su embedding sobre la pseudo esfera definida en R(2,2) al identificar puntos en la superficie. Se integran las ecuaciones de movimiento para sus geodésicas concluyendo que este espacio es geodésicamente incompleto. Con la estructura geodésica se muestra que este espacio es una solución razonable a las ecuaciones de Einstein, con una singularidad quasiregular. Además se estudia la singularidad presente en todos los espacios tipo BTZ a partir de las holonomías que la encierran. Se calculan sus holonomías sobre el espacio tangente ocupando una conexión de SO(2, 1) y luego las holonomías en la teoría de Chern-Simons equivalente ocupando una conexión de SO(2,2). Adicionalmente, se justifica la presencia de una fuente tipo delta de Dirac a partir de la existencia de holonomías no triviales en loops infinitesimales, dando una relación explícita entre estas. Por último, se exponen ideas no exploradas en este trabajo, que serán útiles para futuros trabajos.
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    On D5-brane description of 1:4-BPS latitude Wilson loops in the AdS/CFT correspondence
    (2023) Moreno Vilches, Cristobal; Faraggi Ugalde, Alberto Tomás; Bañados, Máximo; Pontificia Universidad Católica de Chile. Instituto de Física
    Motivated by the AdS/CFT correspondence, the gravitational description of the 1/4-BPS latitude Wilson loop in the totally anti-symmetric representation of the gauge group is presented, under the dictionary this correspond to a D5-brane whose dynamics is governed by the DBI action and Weiss-Zumino. The approach we used was to work with the BPS equations coming from demanding the κ-symmetric projection condition on the target space killing spinor. Such equations are of first order in derivatives so in practice easily to solve instead of solving the Euler-lagrange equations coming from varying the action of the brane. In order to preserve all the symmetries that the Wilson loop has, the anzats used produces 16 BPS equations. Such equations were solved and we present the solution and study its properties.
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    Quantum scalar theories in the AdS/CFT correspondence
    (2021) Bianchi Palacios, Ernesto; Bañados, Máximo; Pontificia Universidad Católica de Chile. Instituto de Física
    This thesis contains original research on the conjectured AdS/CFT correspondence. Known are the holographic correlators resulting from this correspondence under its classical approximation, confirming the conjecture at this level. In this work we will explore its consequences beyond this approximation, considering the quantum corrections to these known dual correlators for the particular cases of scalar Phi^3 and Phi^4 theories on a fixed AdS(d+1) background. This will involve the development of a scheme that adds systematically order by order the quantum corrections to the correlators obtained classically together with the computation of these new contributions, introducing on the way sensible regularization and renormalization schemes for the different expected divergences. This process will show in a clear way the effect of these loop corrections through the main role played by the infrared and ultraviolet divergences, which is briefly summarized in: the quantum corrections to the holographic correlators produce anomalies in the resulting CFT in the form of an anomalous scaling dimension, confirming the validity of the conjecture beyond tree-level computations. All this study is carried out throughout this thesis for arbitrary values of the parameters of the theory in the bulk. With the intention to study the general ideas and results developed in this work, at the end of the thesis a particular case is analyzed.