Fibraciones de Cardy
This work is focused on the study of families of open-closed topological fieldtheories parameterized by a manifold with multiplication and their relationshipswith twisted vector bundles. Open-closed field theories were axiomatized by G. Moore and G. Segal in [51]. The study of families of such theor...
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | |
| Formato: | Tesis doctoral publishedVersion |
| Lenguaje: | Inglés |
| Publicado: |
Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales
2015
|
| Materias: | |
| Acceso en línea: | https://hdl.handle.net/20.500.12110/tesis_n5831_Amoreo |
| Aporte de: |
| id |
tesis:tesis_n5831_Amoreo |
|---|---|
| record_format |
dspace |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
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 |
| spellingShingle |
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 Amoreo, Aníbal Fibraciones de Cardy |
| topic_facet |
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 |
| description |
This work is focused on the study of families of open-closed topological fieldtheories parameterized by a manifold with multiplication and their relationshipswith 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 manifoldwith multiplication which generalize the definition of Moore and Segal in thesense that when the base manifold is a one-point space, we recover the originaldefinition. A careful study of their properties (that is, a detailed proof showingthat these categories are additive, pseudo-abelian and enjoy an action of the categoryof locally free modules) led us to a relationship between these families ofopen-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 transitionhomomorphisms of Cardy fibrations and Higgs bundles. The last part deals with global objects (that is, objects of the category over thewhole base space). A functorial link between the category of modules over thespectral cover and the category of modules over the tangent sheaf of the manifoldis 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 thefibred category defined over the whole base space, the space of arrows a!a can bedefined 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 vectorbundles are closely related to these Azumaya algebras. This facts led us to acharacterization of global objects in the fibred category in terms of twisted vectorbundles over the spectral cover of the base manifold. Keywords: Open-closed field theory, twisted vector bundle, manifold withmultiplication, spectral cover, 2-vector bundle. |
| author2 |
Devoto, Jorge A. |
| author_facet |
Devoto, Jorge A. Amoreo, Aníbal |
| format |
Tesis doctoral Tesis doctoral publishedVersion |
| author |
Amoreo, Aníbal |
| author_sort |
Amoreo, Aníbal |
| title |
Fibraciones de Cardy |
| title_short |
Fibraciones de Cardy |
| title_full |
Fibraciones de Cardy |
| title_fullStr |
Fibraciones de Cardy |
| title_full_unstemmed |
Fibraciones de Cardy |
| title_sort |
fibraciones de cardy |
| publisher |
Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| publishDate |
2015 |
| url |
https://hdl.handle.net/20.500.12110/tesis_n5831_Amoreo |
| work_keys_str_mv |
AT amoreoanibal fibracionesdecardy AT amoreoanibal cardyfibrations |
| _version_ |
1782022820813864960 |
| spelling |
tesis:tesis_n5831_Amoreo2023-10-02T20:11:55Z Fibraciones de Cardy Cardy fibrations Amoreo, Aníbal Devoto, Jorge A. 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 This work is focused on the study of families of open-closed topological fieldtheories parameterized by a manifold with multiplication and their relationshipswith 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 manifoldwith multiplication which generalize the definition of Moore and Segal in thesense that when the base manifold is a one-point space, we recover the originaldefinition. A careful study of their properties (that is, a detailed proof showingthat these categories are additive, pseudo-abelian and enjoy an action of the categoryof locally free modules) led us to a relationship between these families ofopen-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 transitionhomomorphisms of Cardy fibrations and Higgs bundles. The last part deals with global objects (that is, objects of the category over thewhole base space). A functorial link between the category of modules over thespectral cover and the category of modules over the tangent sheaf of the manifoldis 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 thefibred category defined over the whole base space, the space of arrows a!a can bedefined 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 vectorbundles are closely related to these Azumaya algebras. This facts led us to acharacterization of global objects in the fibred category in terms of twisted vectorbundles over the spectral cover of the base manifold. Keywords: Open-closed field theory, twisted vector bundle, manifold withmultiplication, spectral cover, 2-vector bundle. Este trabajo trata principalmente sobre el estudio de familias de teorías topológicasde campo abiertas-cerradas parametrizadas por una variedad con multiplicacióny su relación con fibrados vectoriales torcidos. Las teorías abiertas-cerradas fueron axiomatizadas por G. Moore y G. Segalen [51]. A partir del estudio de dichas teorías se definieron las nociones de fibraciónde Calabi-Yau y fibración de Cardy; estas son categorías fibradas (en realidadstacks) sobre la variedad con multiplicación en cuestión, que generalizanla definición dada por Moore y Segal, en el sentido de que cuando la variedad basetiene un único punto, se recupera la definición original. Un estudio detallado desus propiedades (aditividad, pseudo-abelianidad y la acción de la categoría de móduloslocalmente libres) nos llevó a obtener una relación entre estas familias deteorías de campos y los 2-fibrados vectoriales de Baas, Dundas y Rognes, dandoasi una respuesta afirmativa a una sugerencia de G. Segal en [57]. Mas aún, seobtuvo también una relación entre los morfismos de transición de la fibración de Cardy y los fibrados de Higgs. La última parte de la tesis estudia principalmente los objetos globales (esto es,los objetos de la categoría definida sobre toda la variedad base). En primer lugar,se obtuvo una relación functorial entre la categoría de módulos sobre el recubrimientoespectral y la de módulos sobre el haz tangente. También mostramos quelas álgebras de Azumaya, en el sentido de A. Grothendieck [29], aparecen naturalmenteen el estudio de las fibraciones de Cardy: dado un objecto a de la categoríadefinido sobre toda la variedad base, el espacio de morfismos a!a se puededefinir como el pushout de cierta álgebra de Azumaya a lo largo de la proyecciónespectral S ! M. Por otro lado, como fue demostrado por M. Karoubi en [35], losfibrados torcidos están íntimamente relacionados con las álgebras de Azumaya. Estos hechos nos llevaron a obtener una caracterización de los objetos globalesde la categoría fibrada en términos de los fibrados torcidos sobre el recubrimientoespectral de la variedad base. Palabras clave: Teoría de campos abierta-cerrada, fibrado vectorial torcido,variedad con multiplicación, recubrimiento espectral, 2-fibrado vectorial. Fil: Amoreo, Aníbal. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales 2015-09-25 info:eu-repo/semantics/doctoralThesis info:ar-repo/semantics/tesis doctoral info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar https://hdl.handle.net/20.500.12110/tesis_n5831_Amoreo |