Generalized Symmetries in the Strong Coupling Limit

This thesis examines applications of generalized symmetries to strongly coupled Yang-Mills theories in four dimensions. We begin by providing a brief overview of recent developments in generalized symmetries, namely higher-form symmetries, non-invertible symmetries, higher-group symmetries, and generalized 't Hooft anomalies. We then proceed to study several examples of their applications in understanding the infrared (IR) behaviour of Yang-Mills theories as they become strongly coupled. Firstly, we study a family of 2-index chiral gauge theories, which exhibit generalized anomalies arising from the presence of fractionally charged backgrounds, known as 't Hooft fluxes (or twists). We leverage the 't Hooft anomalies to constrain their IR phases. In some cases, the generalized anomalies allow us to eliminate the possibility of composite fermions, which was not previously possible with ordinary 't Hooft anomalies. After studying higher-form symmetries, we then proceed to analyze the non-invertible symmetry in Yang-Mills theories arising from 't Hooft twists, and we provide an explicit method to construct such symmetries in the Hamiltonian formalism. Finally, we turn to axion physics and argue that a three-form gauge theory is a good effective field theory description for axion-Yang-Mills in the IR, incorporating both higher-form symmetries and higher-group symmetries.