D=10 Super Yang-Mills, D=11 Supergravity and the Pure Spinor Superfield Formalism
Carregando...
Data
2016-03-07
Autores
Guillen Quiroz, Luis Max [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
E bem conhecido como descrever as teor´ıas de Super Yang-Mills (SYM) ´ em D = 10 dimens˜oes e Supergravidade (SG) em D = 11 dimens˜oes no superespa¸co e via seus campos componentes. No entanto, uma nova vers˜ao desses modelos foi formulada nos finais da d´ecada de 2000, quando Martin Cederwall usando o formalismo de supercampo de espinor puro conseguiu construir uma pure spinor a¸c˜ao, que a diferen¸ca das anteriores abordagens, esta n˜ao precisa de impor constraints a m˜ao, proporciona uma descri¸c˜ao completa de cada modelo (no sentido do formalismo BV) e as equa¸c˜oes do movimento obtidas a partir do respectivo principio de a¸c˜ao s˜ao supersim´etricas. Neste trabalho iremos explicar toda a base necess´aria para entender a constru¸c˜ao de tal formalismo. Para esse prop´osito, come¸caremos estudando a teoria SYM (abeliana) em D = 10 em suas formula¸c˜oes em componentes e no superespa¸co. Usaremos a a¸c˜ao da formula¸c˜ao on-shell para quantizar a teoria via o formalismo de Batalin-Vilkovisky (BV). Seguiremos para SG em D = 11 e estudaremos suas formula¸c˜oes em componentes e no superespa¸co. Ent˜ao iremos mostrar que podemos obter o mesmo espectro f´ısico de SYM em D = 10 (SG em D = 11) estudando a superpart´ıcula em D = 10 (D = 11) na calibre do cone de luz. De forma a ter uma quantiza¸c˜ao covariante desses modelos, introduziremos a superpart´ıcula de espinor puro em D = 10 (D = 11), a qual possui o operador BRST usual de espinor puro (Q = λD). Verificar-se-´a que a cohomologia desse operador coincidir´a com a teoria SYM em D=10 (SG em D=11) linearizada depois de ser quantizada via o formalismo BV. Esse resultado introduzir´a naturalmente a ideia de construir a¸c˜oes usando um supercampo de espinor puro. Finalmente, explicaremos como o formalismo de supercampo de espinor puro surge nesse contexto e como podemos us´a-lo para construir a¸c˜oes manifestamente supersim´etricas para SYM em D=10 e SG em D=11.
It is well known how to describe the D = 10 (SYM) Super Yang-Mills and D = 11 (SG) Supergravity theories on superspace and by component fields. However, a new version of these models was formulated in the late 2000, when Martin Cederwall using the pure spinor superfield formalism achieved to construct a pure spinor action for these theories, which unlike the previously mentioned approaches, this does not require to impose any constraint by hand, provides a full description of each model (in the BV sense) and the equations of motion coming from the corresponding action principle are supersymmetric. In this work we will explain all the background required to understand the construction of this action. For this purpose, we will start with the D=10 (abelian) SYM theory in its component and superspace formulations. We will use the action of the on-shell formulation to quantize the theory via the Batalin-Vilkovisky framework. We will move to D=11 supergravity and study its component and superspace formulations. Then we will show that we can obtain the same physical spectrum of D = 10 SYM (D = 11 SG) by studying the D = 10 (D = 11) superparticle in the light-cone gauge. In order to have a covariant quantization of these models, we will introduce the D = 10 (D = 11) pure spinor superparticle, which possesses the usual pure spinor BRST operator (Q = λD). It will turn out that the cohomology of this operator will coincide with the linearized D = 10 SYM (D = 11 SG) theory after being quantized via BV-formalism. This result will introduce naturally the idea of constructing pure spinor actions. Finally, we will explain how the pure spinor superfield framework arises in this context and how we can use it to construct manifestly supersymmetric actions for D = 10 SYM and D = 11 SG.
It is well known how to describe the D = 10 (SYM) Super Yang-Mills and D = 11 (SG) Supergravity theories on superspace and by component fields. However, a new version of these models was formulated in the late 2000, when Martin Cederwall using the pure spinor superfield formalism achieved to construct a pure spinor action for these theories, which unlike the previously mentioned approaches, this does not require to impose any constraint by hand, provides a full description of each model (in the BV sense) and the equations of motion coming from the corresponding action principle are supersymmetric. In this work we will explain all the background required to understand the construction of this action. For this purpose, we will start with the D=10 (abelian) SYM theory in its component and superspace formulations. We will use the action of the on-shell formulation to quantize the theory via the Batalin-Vilkovisky framework. We will move to D=11 supergravity and study its component and superspace formulations. Then we will show that we can obtain the same physical spectrum of D = 10 SYM (D = 11 SG) by studying the D = 10 (D = 11) superparticle in the light-cone gauge. In order to have a covariant quantization of these models, we will introduce the D = 10 (D = 11) pure spinor superparticle, which possesses the usual pure spinor BRST operator (Q = λD). It will turn out that the cohomology of this operator will coincide with the linearized D = 10 SYM (D = 11 SG) theory after being quantized via BV-formalism. This result will introduce naturally the idea of constructing pure spinor actions. Finally, we will explain how the pure spinor superfield framework arises in this context and how we can use it to construct manifestly supersymmetric actions for D = 10 SYM and D = 11 SG.
Descrição
Palavras-chave
Supersimetría, Super Yang Mills, Supergravidade, Espinores Puros, Supersymmetry, Supergravity, Pure spinors