Teoria de calibre em variedades de holonomia especial

Author(s)

Rodrigo de Menezes Barbosa

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2013-06-27

Examining board members

Marcos Benevenuto Jardim; Henrique Nogueira de Sá Earp; Henrique Bursztyn

• Advisor: Marcos Benevenuto Jardim

Abstract

In this work we study gauge theory on high dimensional manifolds with emphasis on Calabi-Yau, G2 and Spin(7) manifolds. We start by developing the theory of connections on fiber bundles and their associated holonomy groups, culminating with Berger's theorem classifying the holonomies of RIemannian manifolds and Wang's theorem relating the holonomy groups to the existence of parallel spinors. We proceed to describe in more detail the geometric structures resulting from holonomy reduction, including topological (homology and fundamental group) and geometric (curvature) aspects. In the last chapter we develop the formalism of gauge theory in dimension four: we introduce the moduli space of instantons and the dimensional reductions of the anti-selfduality equations. With this motivation in mind, we proceed to study gauge theories on manifolds of special holonomy and also some of their dimensional reductions (AU)

• FAPESP's process: 11/04214-0 - Gauge theories and topological invariants
• Grantee: Rodrigo de Menezes Barbosa
• Support Opportunities: Scholarships in Brazil - Master