Title: Dualities and the Geometric View of Theories
Abstract:
In the recent literature on the semantic conception, it has been argued that a bare collection of models subject to kinematical or dynamical conditions is not sufficient to define a theory: additional structure on the space of models is required. In this talk, I will develop a geometric view of theories, according to which a physical theory is a structured space of models equipped with topological and geometric structure, typically organised by a moduli space. Building on this, I propose a more specific framework, the model bundle, in which putative ‘theories’ are models (fibres) of a higher‑level structure. The fibres contain states and quantities, the base is a moduli space, and a structure group of quasi-dualities acts on the fibres; the total space thereby carries natural geometric structure. I will illustrate this with S-duality in the Seiberg-Witten theory, where the moduli space is the complex plane with three punctures and the modular group acts as the structure group. Quasi‑dualities are local transition functions between fibres; when the bundle is trivial, dualities are recovered as global transition functions. I will also discuss how the geometric view bears on discussions of T-duality.