Theses
THESIS DEFENSE -- Moduli of higher connections and holomorphic 2-Bundles
Speaker: Roberto Téllez Domínguez (ICMAT-UAM)Advisor/s: Luis Álvarez Cónsul (ICMAT-CSIC) & Mario García Fernández (ICMAT-CSIC)Date: Monday, 05 May 2025 - 10:00Place: Aula Naranja, ICMAT
Abstract:
In this thesis we study the geometry of moduli spaces associated to principal 2-bundles. We consider Lie 2-groups G that arise from a Lie group with an Ad-invariant, symmetric, bilinear form on its Lie algebra. In this setting, we construct derived moduli stacks of flat G-connections over a smooth manifold, holomorphic G-bundles over a complex manifold and holomorphic G-bundles with holomorphic connective structure over a complex manifold. We introduce dilaton derived moduli and use them to obtain canonical shifted symplectic structures on these derived stacks, which are naturally identified with the derived critical locus of the heterotic superpotential. For this, we relate holomorphic G-bundles with holomorphic connective structures to solutions of the Hull-Strominger system appearing in supersymmetric string theory.
