It’s been known since the work of Callan and Rubakov that a generic gauge theory harbours a riddle: the scattering of light fermions off heavy magnetic monopoles necessitates exotic outgoing states, seemingly with fractional occupation numbers. I will first explain how we can make sense of these outgoing states in the modern language of generalised symmetries: They are created by operators living at the edge of a topological surface, and in turn correspond to states in a particular twisted Hilbert space. I will then apply this general formalism to the original case of interest, the Standard Model itself, where the resulting states turn out to carry fractionalised baryon and lepton numbers. I will finally discuss various other scenarios, including some that require non-invertible symmetry defects.

TBA

Since the existence of interacting SCFTs in six dimensions was first inferred by string theory, many have sought a Lagrangian construction of such models. With this goal in mind, in this talk I will introduce some curious supersymmetric Lagrangian gauge theories in five dimensions. These models exhibit an Omega-deformed non-relativistic conformal symmetry, and have a single, discrete coupling. Crucially, I will argue that these models in fact capture the dynamics of six-dimensional (2,0) and (1,0) SCFTs, through a solitonic enhancement mechanism analogous to that of the ABJM model. I will finally speculate on the utility of the models, including through the fashionable paradigms of integrability and localisation.