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Título de Acceso Abierto
Fibraciones de Cardy
Aníbal Amoreo Jorge A. Devoto
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Resumen/Descripción – provisto por el repositorio digital
This work is focused on the study of families of open-closed topological field theories parameterized by a manifold with multiplication and their relationships with twisted vector bundles. Open-closed field theories were axiomatized by G. Moore and G. Segal in [51]. The study of families of such theories led us to the definition of Calabi-Yau and Cardy fibrations; these are fibred categories (in fact stacks) over the base manifold with multiplication which generalize the definition of Moore and Segal in the sense that when the base manifold is a one-point space, we recover the original definition. A careful study of their properties (that is, a detailed proof showing that these categories are additive, pseudo-abelian and enjoy an action of the category of locally free modules) led us to a relationship between these families of open-closed field theories and 2-vector bundles (as defined by Baas, Dundas and Rognes in [10]), thus providing an affirmative answer to a suggestion given by G. Segal in [57]. Moreover, we also found a relationship between the transition homomorphisms of Cardy fibrations and Higgs bundles. The last part deals with global objects (that is, objects of the category over the whole base space). A functorial link between the category of modules over the spectral cover and the category of modules over the tangent sheaf of the manifold is obtained. We also show that Azumaya algebras, in the sense of A. Grothendieck [29], appear naturally in the study of Cardy fibrations: given an object a of the fibred category defined over the whole base space, the space of arrows a!a can be defined as the pushout of a certain Azumaya algebra along the spectral projection S ! M. On the other hand, as was proved by M. Karoubi in [35], twisted vector bundles are closely related to these Azumaya algebras. This facts led us to a characterization of global objects in the fibred category in terms of twisted vector bundles over the spectral cover of the base manifold. Keywords: Open-closed field theory, twisted vector bundle, manifold with multiplication, spectral cover, 2-vector bundle.Palabras clave – provistas por el repositorio digital
TEORIA DE CAMPOS ABIERTA-CERRADA; FIBRADO VECTORIAL TORCIDO; VARIEDAD CON MULTIPLICACION; RECUBRIMIENTO ESPECTRAL; 2-FIBRADO VECTORIAL; OPEN-CLOSED FIELD THEORY; TWISTED VECTOR BUNDLE; MANIFOLD WITH MULTIPLICATION; SPECTRAL COVER; 2-VECTOR BUNDLE
Disponibilidad
| Institución detectada | Año de publicación | Navegá | Descargá | Solicitá |
|---|---|---|---|---|
| No requiere | 2015 | Biblioteca Digital (FCEN-UBA) (SNRD) |
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Información
Tipo de recurso:
tesis
Idiomas de la publicación
- español castellano
País de edición
Argentina
Fecha de publicación
2015-09-25
Información sobre licencias CC