Dualities and Categorical Structures from 2D Up

Abstract

A fundamental step towards studying string theory vacua, and, ultimately, their stability, is that of understanding the underlying mathematical structure of the QFT resulting from its dimensional reduction on Calabi-Yau (CY) manifolds, the latter being complex manifolds admitting a category theory description. The present work aims at addressing this question in the case of lower-dimensional gravitating systems, and supersymmetric quiver gauge theories, highlighting the role played by dualities and categorical structures towards studying analytical structures of amplitudes. (Based on the author's PhD thesis. For the official version, submitted for dissertation in January 2024, please see https://www.repository.cam.ac.uk/items/1b4cfbcf-7fcf-415d-a252-ba60f7586899)