Würzburg Seminar on Quantum Field Theory and Gravity

I will present 3 higher-spin extensions of the BMS algebra and its generalisations. The first extension exhibits conformal properties reminiscent of the singleton in Anti-de Sitter space. The second acts on the space of radiative solutions of the d’Alembert equation, i.e. on Sachs’s representation of BMS, which we relate to the scalar massless Poincaré representation and extend to any Carrollian manifold. The third extension arises from the flat/ultrarelativstic limit of the AdS/CFT higher-spin algebra. Along the way, we provide a pedagogical introduction to Carrollian geometry and its relation to BMS.