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Master's Dissertation
DOI
10.11606/D.43.2018.tde-08102018-150801
Document
Author
Full name
Carlos Bercini Vargas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Trancanelli, Diego (President)
Minahan, Joseph
Vieira, Pedro Gil Martins
Title in Portuguese
Estudos sobre teorias quânticas de campos integráveis em duas dimensões
Keywords in Portuguese
Teoria quântica de campos; integrabilidade; supersymmetria; duas dimensões; espalhamento
Abstract in Portuguese
Esta dissertação de mestrado consiste de uma revisão sobre teorias quânticas de campos integráveis em duas dimensões, explorando tanto aspectos clássicos como aspectos quânticos dessas teorias munidas de infinitas cargas conservadas. Em nível clássico, consideramos uma teoria de supercampos escalares em duas dimensões com superpotencial arbitrário. Através da imposição da não produção de partículas a nível-árvore, restringimos a forma das interações adimissíveis, recuperando uma extensão supersimétrica do modelo de sinh-Gordon, o qual é provado ser integrável não somente através da obtenção do conjunto infinito de cargas conservadas, mas também através de S-matrix bootstrap. Ainda no nível clássico também mostramos uma profunda relação entre as Toda theories e os conformal minimal models, a qual se estende para nível quântico onde obtemos uma família de fluxos de renormalização entre os unitary conformal minimal models conhecida como staircase model.
Title in English
Studies in two-dimensional integrable quantum field theories
Keywords in English
quantum field theory; integrability; supersymmetry; two dimensions; scattering
Abstract in English
This master thesis is an overview of integrability in two-dimensional field theories. We explore both classical and quantum aspects of these theories which are characterized by infinitely many conserved charges. At the classical level, we consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree-level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric extension of the sinh-Gordon model. This model is proven to be integrable not only by explicitly finding the infinite set of conserved charges but also via the S-matrix bootstrap. We also show a deep relation between Affine Toda theories and conformal minimal models, that extends to the quantum level, where we find a family of integrable renormalization group flows between the unitary conformal minimal models, known as the staircase model.
 
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MThesisvfinal.pdf (1.23 Mbytes)
Publishing Date
2018-10-08
 
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