Dualities and Symmetries of Quantum Field Theories from Brane Engineering

Abstract: This dissertation presents a study of dualities and generalized global symmetries in quantum field theories (QFTs) from the string theory perspective. Chapter 2 is based on the work arXiv:2110.03696 with Sebasti\'{a}n Franco, Alessandro Minino and \'{A}ngel M. Uranga . It introduces a new class of string theory backgrounds, Spin(7) orientifolds, allowing for the engineering of 2$d$ $\mathcal{N}=(0,1)$ gauge theories on D1-branes and illustrating the perspective on 2$d$ $\mathcal{N}=(0,1)$ theories as real slices of 2$d$ $\mathcal{N}=(0,2)$ ones. Chapter 3 is based on the work arXiv:2112.03929 with Sebasti\'{a}n Franco, Alessandro Minino and \'{A}ngel M. Uranga. It presents a new, geometric perspective on the triality of 2$d$ $\mathcal{N}=(0,1)$ gauge theories, based on their brane engineering introduced in Chapter 2. It also shows that general Spin(7) orientifolds extend triality to theories consisting of coupled 2$d$ $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,1)$ sectors, leading to extensions of triality that interpolate between pure 2$d$ $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,1)$ cases. Chapter 4 is based on the work arXiv:2212.09743 with Jonathan J. Heckman, Max Hubner, Ethan Torres and Hao Y. Zhang. It presents a top-down construction of non-invertible duality symmetries in 4$d$ QFTs. The realization of QFTs is through D3-branes probing a Calabi-Yau threefold with an isolated singularity. The non-invertible duality defect then arises from configurations of 7-branes "at infinity". The study shows that different field-theoretic realizations of duality defects simply amount to distinct choices of where to place 7-brane branch cuts in the 5D bulk.