Fractional-charge hadrons and leptons to tell the Standard Model group apart

Generalised symmetries have expanded our insight into theory but their impact has not fully translated into phenomenology yet. This talk will present a case study that bridges the two fields and aims at being approachable from either end. The gauge group of strong and electroweak interactions in Nature could be any of the four that share the same Lie algebra but have different one form discrete symmetries. Each of these cases allows in its spectrum for the matter fields of the SM but also for new distinctive representations which follow a group-dependent electric charge quantisation rule.