Generalized Symmetries and Compact Models
When coupling quantum field theories (QFTs) to each other and gravity their symmetries are believed to be gauged or broken. We consider this process for supersymmetric QFTs engineered in M-theory by local geometries of special holonomy and characterize the breaking and gauging of their higher symmetries. Here, the coupling of theories is geometrized by the embedding of local models into one compact model where topological data of the embedding determines the fate of n-form and n-group symmetries. With local and global K3 surfaces we take our starting point in 7d. We analyze the global structure of the resulting supergravity gauge group, generalizing and simplifying methods centered on Morrell-Weil groups for elliptic K3s, and give results for torus orbifolds. Next, we consider Calabi-Yau threefolds geometrizing couplings between localized 5d supersymmetric conformal sectors and determine the fate of their generalized symmetries.