Strongly-coupled QFTs from string theory

Strongly-coupled regimes of quantum field theory (QFT) are notoriously challenging to explore. In this thesis, which is divided into two parts, I address the question from a string theoretic perspective. I will focus on methods to map out the RG-flow, symmetries and phase structure, first taking a holographic point of view, then within the context of geometric engineering and brane-webs. Holography constitutes a profound and potent way to describe strongly-coupled QFTs, especially when combined with sophisticated geometric techniques, and modern tools from QFT such as generalized global symmetries and their 't Hooft anomalies. In chapter 3 I will present our work on the gravitational dual of I/c-extremization for a 1d/2d N=(0,2) theory in the presence of a holomorphically varying axio-dilaton. This generalization makes the analysis suitable for F-theory supergravity solutions, and establishes a correspondence of the two extremization principles furnished by M/F-theory duality. In chapter 4 we develop new holographic methods to compute anomalies of discrete higher-form symmetries, and derive the topological field theory (TFT), which matches these anomalies in the infra-red (IR). This interplay of holography and generalized global symmetries shines new light on the topological sector of supergravity theories and its physical implications. We illustrate the approach in a rich non-conformal holographic setting, which flows to confining N=1 SU(N) Super-Yang Mills (SYM) in the IR, focusing on the 1-form symmetry and its mixed 0-/1-form symmetry anomaly, which is closely related to chiral symmetry breaking in gapped confining vacua. Geometric engineering and brane-webs enable us to realize a vast array of superconformal field theories (SCFTs) whose salient features would otherwise be out of reach. In my research, I have focused on 5d N=1 SCFTs, which are intrinsically non-perturbative. In chapters 6 and 7 we establish a comprehensive description of 5d SCFTs in terms of Generalized Toric Polygons (GTPs) and map out their moduli space. Using the duality with brane-webs and insights from toric geometry we parametrize the extended Coulomb branch (CB) and determine an algorithm to compute the magnetic quiver (MQ) describing the Higgs branch (HB). We then apply these methods to all 5d SCFTs that flow to single gauge node theories in the IR with anti-symmetric and fundamental matter. Finally, in chapter 8 we identify a correspondence between 5d extended CB deformations and 3d Fayet-Iliopoulos (FI) deformations in the MQ, which elucidates how changes in the geometry of the HB are implemented as we move along the extended CB.