Dualities and Categorical Structures from 2D Up

TL;DR

This paper explores the mathematical structures, including dualities and categories, underlying 2D quantum field theories derived from string theory compactifications, aiming to understand their analytical properties and stability.

Contribution

It introduces a categorical framework for analyzing 2D gravitating systems and supersymmetric quiver gauge theories, emphasizing dualities' role in amplitude analysis.

Findings

Categorical structures elucidate dualities in 2D QFTs

New insights into the analytical properties of string-derived theories

Framework aids in studying stability of string vacua

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)