The geometry of gauged (super)conformal mechanics

Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, uncover classes which are only scale invariant their ungauged form and become fully conformally after gauging. In these cases the target space gauged model satisfies deformation well-known geometry constraints. We consider bosonic as well $\mathcal{N} = 1,2,4$ supersymmetric extensions. solve quantum ordering ambiguities implementing (super-) symmetry on physical Hilbert space. Examples our general results furnished $D(2,1;0)$-invariant Coulomb branch quiver relevant for black hole physics.