BV formalism and string theory
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Data
2022-05-25
Autores
Viana, Eggon
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Universidade Estadual Paulista (Unesp)
Resumo
Essa tese consiste de basicamente duas partes. Primeiro, serão revisados conceitos basicos e fundamentais de teorias de campos e de cordas. Será dada uma ênfase na ideia de simetria presente em teorias de campos, por exemplo simetrias de calibre, de Poincaré e supersimetria. Será discutido o método BRST de quantização de teorias de calibre, o formalismo de cordas bosonicas de Green- Schwartz e também o formalismo de Pure spinor para supercordas. Tanto o caso plano quanto curvo - AdS5 × S 5 - será tratado. A segunda parte da tese consiste em estudar o formalismo BV e aplicá-lo para descrever teorias que possuem operador BRST, como é o caso da teorias de cordas bosonica e teorias de Yang-Mills. Serão apresentadas descent equations que acabam aparecendo no formalismo BV e com estas equações, serão derivados algumas expressões de operatores de vertex para cordas bosonicas. No final, será feita a descrição da supercordas no formalismo de pure spinor utilizando o formalismo BV, no qual deduzimos expressões de vertex operators não integrados.
This thesis consists basically of two parts. First, we review the most basic and important concepts present in field theory and string theory. We give some focus in discussing the idea of symmetries present in field theories, remarkable gauge symmetry, Poincaré and supersymmetry. We discuss the BRST process of quantizing gauge theories, the formalism of Green-Schwartz for describing fermionic strings and subsequently the pure spinor superstring, both in flat and AdS5 × S 5 background. The second part of the thesis consists in studying the BV formalism and applying it to describe some theories which possesses BRST operators, like bosonic string and Yang Mills. We present descent equations that appears in the BV formalism and show how we can derive vertex operators from it. At the end, we present a the BV description for pure spinor string, in which case we have also derived expressions for vertex operators.
This thesis consists basically of two parts. First, we review the most basic and important concepts present in field theory and string theory. We give some focus in discussing the idea of symmetries present in field theories, remarkable gauge symmetry, Poincaré and supersymmetry. We discuss the BRST process of quantizing gauge theories, the formalism of Green-Schwartz for describing fermionic strings and subsequently the pure spinor superstring, both in flat and AdS5 × S 5 background. The second part of the thesis consists in studying the BV formalism and applying it to describe some theories which possesses BRST operators, like bosonic string and Yang Mills. We present descent equations that appears in the BV formalism and show how we can derive vertex operators from it. At the end, we present a the BV description for pure spinor string, in which case we have also derived expressions for vertex operators.
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Palavras-chave
Teoria de campos (Física), Modelos de corda, Teoria das supercordas