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Master's Dissertation
DOI
https://doi.org/10.11606/D.43.2013.tde-17102014-160000
Document
Author
Full name
Dhyan Victor Hiromitsu Kuraoka
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Trancanelli, Diego (President)
Nastase, Horatiu Stefan
Rivelles, Victor de Oliveira
Title in Portuguese
Laços de Wilson supersimétricos na correspondência AdS/CFT
Keywords in Portuguese
Cordas em AdS
Correspondência AdS/CFT
Laços de Wilson
Modelos de matrizes
Teoria de cordas
Teorias de calibre supersiméticos
Abstract in Portuguese
O objetivo desta dissertação é revisar os operadores laços de Wilson no contexto da correspondência AdS/CFT. Estes operadores, presentes em qualquer teoria de calibre, são importantes por nos fornecer um parâmetro de ordem para a transição de fase confinante/desconfinante. Além disso, eles são particularmente importantes no estudo da correspondência AdS/ CFT pois: i) Eles nos dão, em alguns casos, resultados exatos graças ao fato de poderem ser localizados em um modelo de matrizes, desta forma nos permitindo fazer testes altamente não triviais da correspondência; ii) Eles são os objetos da teoria de calibre que são duais as cordas propagando no interior do espaço, nos dando um rico dicionário entre quantidades no interior (AdS) e na borda do espaço (CFT). Depois de revisarmos os laços de Wilson em teorias de calibre e a correspondência Ads/CFT, introduziremos a definição dos laços de Wilson supersimétricos 1/2 BPS. Calcularemos eles para o caso de um acoplamento fraco e para qualquer outro valor da constante de acoplamento usando técnicas de modelos de matrizes. Finalmente, compararemos nossos resultados com computações de superfícies minimais no interior do espaço, encontrando uma concordância perfeita.
Title in English
Supersymmetric Wilson loops in the AdS/CFT correspondence
Keywords in English
AdS/CFT correspondence
matrix models
String theory
strings in AdS space
Supersymmetric gauge theories
Wilson loops
Abstract in English
The aim of this thesis is to review Wilson loop operators in the contexto f the AdS/CFT correspondence. These operators, wich are present in any gauge theory, are important because they furnish an order parameter for confinement/deconfinement phase transitions. Besides this, they are particularly relevant in the study of the AdS/CFT correspondence because: i) they allow, in some cases, for exact results thanks to localization to matrix models and make it possible to perform highly non-trivial tests of the correspondence; ii) they are the gauge theory objects dual to strings propagating in the bulk of the space and give a rich dictionary between bulk (AdS) and boundary (CFT) quantities. After reviews of Wilson loops in gauge theories and of the Ads/CFT correspondence, we will introduce the definition of 1/2 BPS supersymmetric Wilson loops, we will compute them at weak coupling and then at any order in the coupling constant via matrix model techniques, and finally we will compare our results with minimal surface computations in the bulk, finding perfect agreement.
 
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54686Kuraoka.pdf (866.23 Kbytes)
Publishing Date
2014-10-21
 
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