Week 17.06.2024 – 23.06.2024

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.

This talk will review recent results on the construction of U(1) duality-invariant nonlinear models for gauge (2n-1)-forms in d = 4n dimensions, including $T \bar T$-like flows in the space of such theories. In the four-dimensional case, we will briefly discuss the following U(1) duality-invariant nonlinear systems: (i) models for N-extended superconformal higher-spin multiplets; (ii) the low-energy effective action for N = 4 SYM on its Coulomb branch; and (iii) models for spontaneously broken local N=1 supersymmetry. If time permits, a new formulation for a self-interacting chiral gauge 2n-form in d = 4n + 2 dimensions will be discussed.