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Doctoral Thesis
DOI
https://doi.org/10.11606/T.43.2022.tde-17082022-132640
Document
Author
Full name
Gabriel Nicolaz Nagaoka
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2022
Supervisor
Committee
Trancanelli, Diego (President)
Griguolo, Luca
Melnikov, Dmitry
Rivelles, Victor de Oliveira
Silva, Guillermo Ariel
Title in Portuguese
Estudos de Laços de Wilson em Teorias 3d Chern-Simons-Matter
Keywords in Portuguese
ABJ(M)
Bootstrap Superconforme
Displacement-Multiplet
Função Bermsstrahlung
Laços de Wilson
Abstract in Portuguese
Nesse trabalho nós apresentamos alguns novos deseonvolvimentos no estudo de laços de Wilson em teorias de Chern-Simons-matter em 3d. Nós começamos com uma breve introdução das teorias N = 4 e N = 6 em 3d e a definição de seus operadores de Wilson BPS. Primeiramente, uma nova formulação do laço 1/2-BPS é apresentada, tal formulação aborda e resolve alguns dos problemas da formulação original, como a dependência explcita no parâmetro do contorno e a definição do operador em termos do traço de uma superconexão, ao invés de um super-traço. Essa nova formulação também elucida o espaço moduli desses operadores, que é o conifold. Em seguida, nós consideramos deformações do tipo wavy dos operadores de Wil- son 1/2-BPS de ABJ(M) e os relacionamos à função de Bremsstrahlung de ABJ(M). Nós computamos esses novos operadores com um contorno deformado em primeira ordem em teoria de perturbação. Por fim, a linha de Wilson 1/2-BPS de N = 4 é estudada como um defeito, onde definimos o multipleto de deslocamento em termos de supercampos quirais de su(1, 1|2) e estudamos funções de correlação de 2pt e 4pt via o programa de bootstrap. Os blocos superconformes são derivados por meio da técnica de super- Casimir, e a CFT data é extrada a strong coupling. Nós discutimos a descrição holográfica de defeitos em termos de teoria de cordas tipo IIA em 10d e M2-branes na descrição 11d.
Title in English
Studies of Wilson Loops on 3d Chern-Simons-Matter Theories
Keywords in English
ABJ(M)
Bremsstrahlung Function
Displacement-Multiplet
Superconformal Bootstrap
Wilson Loops
Abstract in English
In this work we present some new developments in the study of Wilson loops in 3d Chern-Simons-matter theories. We begin with a brief introduction of the N = 4 and N = 6 3d theories and the definition of their BPS Wilson operators. Firstly, a new formulation of the 1/2-BPS Wilson loop is provided, which addresses some of the shortcomings of the original formulation, such as the explicit dependence on the contour parameter and the definition of the operator in terms of the trace of a superconnection, rather than a super-trace. This new formulation also elucidates the moduli space of this operators which is the conifold. Secondly, we consider wavy deformations of the 1/2-BPS Wilson loop of ABJ(M) and relate them to the Bremsstrahlung function of ABJ(M). We compute these new loops with a deformed contour to leading order in perturbation theory. Finally, the 1/2-BPS Wilson line of N = 4 is studied as a defect, where we define the displacement multiplet in terms of chiral superfields of su(1, 1|2) and study 2pt and 4pt correlation functions via a bootstrap approach. The superconformal blocks are derived with the super-Casimir approach, and the CFT data is extracted at strong coupling. We comment on the holographic description of defects in terms of type IIA strings in 10d and M2-branes in the 11d description.
 
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NagaokaThesis.pdf (1.50 Mbytes)
Publishing Date
2022-10-18
 
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