Aspects of duality

TL;DR

This thesis explores various dualities across quantum field theories and string theory, focusing on topological theories, 2D sigma models, and nonperturbative string dualities, highlighting their interrelations and underlying principles.

Contribution

It provides a comprehensive analysis of dualities in different theoretical frameworks, proposing the consistency condition that renormalization group flows and T-duality should commute in 2D sigma models.

Findings

Duality in topological quantum field theories related to four-manifolds

Interplay between RG flows and T-duality in 2D sigma models

Review of nonperturbative dualities in string theory

Abstract

This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual) approaches to the study of four-manifolds. Lower-dimensional variants of these theories are also discussed. In the second part of the thesis we discuss duality in 2D sigma models by studying the interplay between renormalization group flows - as generated by the beta functions - and T-duality. The hypothesis put forward in the thesis is that for these to be mutually consistent, they should commute as operators in parameter space. The last part of the thesis bring these subjects into perspective by reviewing some nonperturbative dualities in string theory.