Electroweak symmetries from the topology of deformed spacetime with minimal length scale

Abstract: Lie-type deformations provide a systematic way of generalising the symmetries of modern physics. Deforming the isometry group of Minkowski spacetime through the introduction of a minimal length scale $\ell$ leads to anti de Sitter spacetime with isometry group $SO(2,3)$. Quantum spacetime on scales of the order $\ell$ therefore carries negative curvature. Considering extended particles of characteristic size $\ell$ carrying topological information and requiring that their topological properties be compatible with those of the underlying spacetime, we show that electroweak symmetries emerge from the maximal compact subgroup of the anti de Sitter isometry group in a way that is consistent with no-go theorems. It is speculated that additional deformation outside the Lie-algebraic framework, such as $q$-deformations, could likewise provide an explanation of the origin of the strong force.